Ellipse11 questions

Ellipse — JEE Maths Practice Questions & Solutions

11 questions on Ellipse with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

(3,3)

and

(-4,4)

and passing through the origin has eccentricity equal to:

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medium

The foci of an ellipse are

(-2,4)

and

(2,1)

. The point

\left(1,\dfrac{23}{6}\right)

is an extremity of the minor axis. What is the value of the eccentricity?

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medium

An ellipse with major and minor axes of length

10\sqrt3

and

10

units slides along the coordinate axes and always remains confined in the first quadrant. The locus of the centre of the ellipse is the arc of a circle. The length of this arc is:

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easy

The equation

\dfrac{x^2}{10-a}+\dfrac{y^2}{4-a}=1

represents an ellipse if:

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easy

The eccentricity of the ellipse

(x-3)^2+(y-4)^2=\dfrac{y^2}{9}

is:

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easy

An ellipse has foci at

(9,20)

and

(49,55)

in the

xy

-plane and is tangent to the

x

-axis. The length of its major axis is:

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easy

\dfrac{x^2}{f(4a)}+\dfrac{y^2}{f(a^2-5)}=1

represents an ellipse with major axis as

y

-axis and

f

is a decreasing function, then

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easy

b^2=a^2(1-e^2)

, then for any

\alpha

a,b\in\mathbb{R}

\sqrt{a^2\cos^2\alpha+b^2\sin^2\alpha-2a^2e\cos\alpha+a^2e^2}+\sqrt{a^2\cos^2\alpha+b^2\sin^2\alpha+2a^2e\cos\alpha+a^2e^2}

is equal to:

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easy

If an ellipse slides on the rectangular coordinate axes and foci of the ellipse are at

(2,y_1)

and

(3,y_2)

, then

y_1y_2

equals

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easy

The foci of the ellipse

3x^2-4xy+3y^2=5

\left\{(r+5-4|\cos\theta|)^2+(r-3|\sin\theta|)^2\right\}

\forall\,r,\theta\in\mathbb{R}

, is:

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