Q JEE MAIN 2020

If the common tangent to the parabolas, $y^2=4 x$ and $x^2=4 y$ also touches the circle, $x^2+y^2=c^2$, then c is...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

The length of the chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid point is $\left(1, \frac{2}{5}\right)$, is equal to :

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let C be the circle ${x^2} + {(y - 1)^2} = 2,{E_1}$ and ${E_2}$ be two ellipses whose centres lie...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2, –3) and eccentricity is $\frac{4}{5}$ ,...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

A line passing through the point $P(\sqrt 5 ,\sqrt 5 )$ intersects the ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{25}} = 1$ at...

JEE Main Mathematics Hard

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Q

The equation of the chord, of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$, whose mid-point is $(3,1)$ is :

JEE Main Mathematics Easy

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Q JEE MAIN 2025

If S and S' are the foci of the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{9} = 1$ and P be a point...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

The length of the chord of the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$, whose mid-point is $\left(1, \frac{1}{2}\right)$, is :

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the ellipse ${{\rm{E}}_1}:\frac{{{x^2}}}{{{{\rm{a}}^2}}} + \frac{{{y^2}}}{{\;{{\rm{b}}^2}}} = 1,{\rm{a}} > {\rm{b}}$ and ${{\rm{E}}_2}:\frac{{{x^2}}}{{\;{{\rm{A}}^2}}} + \frac{{{y^2}}}{{\;{{\rm{B}}^2}}} = 1,\;{\rm{A}} < {\rm{B}}$ have same...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let ${{\rm{E}}_1}:\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ be an ellipse. Ellipses ${{\rm{E}}_1}$'s are constructed such that their centres and eccentricities are...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the product of the focal distances of the point $\left( {\sqrt 3 ,\frac{1}{2}} \right)$ on the ellipse $...

JEE Main Mathematics Medium

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