Are these practice questions for Conic Sections based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Conic Sections free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Conic Sections mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Conic Sections for full coverage.

How many practice questions are there for Conic Sections?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Conic Sections Class 11 Mathematics Practice Questions with Answers

easy

Name the conic section obtained when a plane intersects a double-napped cone at an angle

\beta = 90^{\circ}

with the vertical axis of the cone.

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easy

Identify the center and radius of the circle given by the equation

(x - 3)^2 + (y + 5)^2 = 49

.

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easy

Analyze the equation

\frac{x^2}{49} - \frac{y^2}{25} = 1

to find the coordinates of the vertices of the hyperbola.

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easy

Calculate the radius of the circle given by the equation

(x - 5)^2 + (y + 3)^2 = 49

.

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easy

State the standard equation of a parabola with its vertex at the origin and its axis of symmetry along the positive x-axis.

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easy

Propose an argument to explain why the directrix of a parabola can never pass through its focus.

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easy

Define a circle.

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easy

Determine the equation of the directrix for the parabola

y^2 = 14x

.

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easy

Analyze the equation

x^2 = -10y

to find the coordinates of the focus of the parabola.

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medium

Design a plan for an archway in the shape of a semi-ellipse. The base of the arch must be 10 meters wide. A tall vehicle, 2.5 meters high, needs to pass through the arch. To ensure safe passage, the vehicle must be able to drive through at a distance of 1 meter from the outer edge of the arch. Formulate the equation for the arch and calculate the minimum required height at its center.

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medium

For the parabola given by the equation

y^2 = 16x

, list the coordinates of the focus, the equation of the directrix, and the length of the latus rectum.

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medium

Summarize the key properties of a parabola defined by the equation

x^2 = -4ay

, where

a > 0

. Include its vertex, focus, equation of the directrix, axis of symmetry, and the direction it opens.

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medium

What is the relationship between the semi-major axis

a

, the semi-minor axis

b

, and the distance

c

from the center to a focus for an ellipse?

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medium

Describe the standard form of the equation of an ellipse with its center at the origin and major axis along the y-axis. List the formulas for its foci, vertices, eccentricity, and the length of its latus rectum in terms of

a

and

b

.

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medium

Evaluate why a hyperbola has two separate branches while an ellipse is a single closed curve, by considering their respective geometric definitions.

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medium

Solve for the center and radius of the circle defined by the equation

3x^2 + 3y^2 + 6x - 12y - 1 = 0

.

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medium

For the hyperbola

16y^2 - 9x^2 = 144

, analyze the equation to find the coordinates of the foci, the vertices, the eccentricity, and the length of the latus rectum.

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medium

Calculate the equation of the parabola with its vertex at the origin, the axis of symmetry along the y-axis, and passing through the point

(-4, -8)

.

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medium

Prove that for any ellipse

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

(with

a>b

), the length of the latus rectum is

\frac{2b^2}{a}

. Your proof must be derived from the definition and equation of the ellipse.

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medium

Derive the equation of a parabola with its vertex at

(h, k)

and its axis of symmetry parallel to the x-axis, opening to the right.

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medium

Justify why the eccentricity

e

of any parabola is always equal to 1, based on its definition.

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medium

Determine the equation of the ellipse whose foci are at

(0, \pm 6)

and the length of the minor axis is 16.

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medium

Define the eccentricity of a hyperbola.

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medium

Explain the conditions, using the angles

\alpha

and

\beta

, under which the intersection of a plane with a double-napped cone results in (a) an ellipse, (b) a parabola, and (c) a hyperbola. (Here

\alpha

is the angle of the generator with the axis and

\beta

is the angle of the plane with the axis).

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medium

Calculate the eccentricity of the ellipse given by the equation

25x^2 + 9y^2 = 225

.

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medium

A rod of length 12 cm moves with its ends always touching the coordinate axes. A point P on the rod is 4 cm from the end in contact with the x-axis. Derive the equation of the locus of P and identify the conic section.

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medium

Formulate the equation of a circle passing through the origin

(0,0)

and making intercepts

p

and

q

on the x-axis and y-axis respectively. Justify your result.

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medium

Find the equation of the hyperbola with foci at

(\pm 10, 0)

and an eccentricity of

e = \frac{5}{3}

.

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medium

Find the equation of a circle which is concentric with the circle

x^2 + y^2 - 8x + 12y + 15 = 0

and has an area of

25\pi

square units.

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medium

Create a mathematical model for a parabolic reflector. The reflector is designed such that it is 24 cm in diameter and 9 cm deep. Formulate the equation of the parabola and determine the position of its focus.

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medium

Critique the statement: "A circle is a special case of an ellipse." Justify your answer using the standard equation of an ellipse.

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medium

An archway is in the shape of a semi-ellipse. The base of the arch is 10 m wide, and the highest point of the arch is 4 m above the ground. Calculate the height of the arch at a point 2 m from the center of the base.

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medium

Identify the coordinates of the vertices and the foci for the ellipse given by the equation

\frac{x^2}{25} + \frac{y^2}{16} = 1

.

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medium

Describe the major axis and minor axis of an ellipse. State which axis contains the foci.

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hard

Explain the difference between the transverse axis and the conjugate axis of a hyperbola.

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hard

A comet has a hyperbolic orbit with the Sun at one focus. The equation of its path is

\frac{x^2}{144} - \frac{y^2}{400} = 1

, where distances are in millions of kilometers. When the comet is at one of the vertices of its path, how far is it from the Sun? Formulate a general principle for the closest distance of an object in a hyperbolic orbit to the star at its focus.

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hard

A point

P(x, y)

moves such that the sum of its distances from two fixed points

F_1(0, -c)

and

F_2(0, c)

is a constant

2a

, where

2a > 2c

. Derive the equation of the locus of

P

and identify the conic.

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hard

Calculate the equation of the circle that passes through the points

(1, 2)

and

(3, 4)

and whose center lies on the line

3x + y = 11

.

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hard

An equilateral triangle is inscribed in the parabola

y^2 = 4ax

such that one of its vertices is at the vertex of the parabola. Derive the length of a side of this triangle.

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hard

Explain the concept of 'degenerate conic sections'. Describe the three types of degenerate conics and the conditions under which they are formed when a plane intersects the vertex of a cone.

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hard

For the hyperbola

\frac{y^2}{9} - \frac{x^2}{16} = 1

, identify the orientation of the transverse axis and state the length of the latus rectum.

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hard

An equilateral triangle is inscribed in the parabola

y^2 = 8ax

, with one of its vertices at the vertex of the parabola. Calculate the length of a side of the triangle.

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hard

Formulate the condition for the line

y = mx + c

to be tangent to the circle

x^2 + y^2 = r^2

.

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hard

Justify the conditions on the angles

\alpha

and

\beta

that result in the three non-degenerated conic sections (ellipse, parabola, hyperbola), where

\alpha

is the semi-vertical angle of the cone and

\beta

is the angle the cutting plane makes with the cone's axis.

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hard

A parabolic arch has a height of 25 m and a base width of 40 m. Calculate the height of the arch at a horizontal distance of 10 m from the center of the base.

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Conic SectionsClass 11 Mathematics Practice Questions