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JEE • MATHEMATICS • ELLIPSE

Ellipse practice · Medium

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 181-187 of 187 questions

181 Medium

181 of 187

Application +4 | -1

The centre of the ellipse

9{x^2} + 25{y^2} - 18x - 100y - 166 = 0,

View answer and explanation

Correct option: D

\left( {1,2} \right)

Option D ((1,2)) is correct because completing the square allows us to rewrite the ellipse equation and identify the center.

182 Medium

182 of 187

Analyzing +4 | -1

Let

S_1(\alpha, 0)

and

S_2(-\alpha, 0)

be the focii of the ellipse

\frac{x^2}{4}+\frac{y^2}{3}=1,(\alpha > 0)

. If

S=0

be the locus of the image of the focus

S_1

about any tangent on the ellipse, then area bounded by

S=0

and

x+3 y+1=0

is equal to

View answer and explanation

Correct option: C

8 \pi

sq. units

The correct answer is

8 \pi

sq. units because the locus of the image of the focus about any tangent is a circle, and the area bounded by this circle and the given line can be calculated.

183 Medium

183 of 187

Analyzing +4 | -1

From point

P(8,27)

tangents

P Q

and

P R

are drawn to the ellipse

\frac{x^2}{4}+\frac{y^2}{9}=1

. Then, angle subtended by

Q R

at origin is

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the calculated angle subtended by QR at the origin does not match any of the given options. The angle is found by homogenizing the ellipse equation.

184 Medium

184 of 187

Application +4 | -1

The locus of chords of contact of perpendicular tangents to the ellipse

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

touch another fixed ellipse is

View answer and explanation

Correct option: C

\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{\left(a^2+b^2\right)}

Option C (

\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{\left(a^2+b^2\right)}

) is correct because it represents the equation of the fixed ellipse touched by the chords of contact of perpendicular tangents to the given ellipse.

185 Medium

185 of 187

Application +4 | -1

The line

3x + 5y = 15\sqrt 2

is a tangent to the ellipse

\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1,

at a point whose eccentric angle is

View answer and explanation

Correct option: B

\frac{\pi }{4}

Option B (

\frac{\pi}{4}

) is correct because by comparing the given tangent equation with the parametric form of the tangent to the ellipse, we can find the eccentric angle.

186 Medium

186 of 187

Application +4 | -1

Equation of the ellipse with eccentricity

\frac{1}{2}

and foci at

\left( { \pm \,1,0} \right)

View answer and explanation

Correct option: B

\frac{{{x^2}}}{4} + \frac{{{y^2}}}{3} = 1

Option B (

\frac{{{x^2}}}{4} + \frac{{{y^2}}}{3} = 1

) is correct because it represents the equation of an ellipse with the given eccentricity and foci.

187 Medium

187 of 187

Application +4 | -1

The radius of the circle passing through the foci of the ellipse

\frac{{{x^2}}}{4} + \frac{4}{7}{y^2} = 1

and having its centre at

\left( {\frac{1}{2},\;2} \right)

, is

View answer and explanation

Correct option: A

\sqrt 5

Option A (

\sqrt 5

) is correct because the radius is calculated using the distance formula between the focus and the center of the circle.

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