Equation of ellipse whose latus rectum is 8 and whose eccentricity is frac{1}{{√ 2 }} , referred t

English

Gujarati

Hindi

10-2. Parabola, Ellipse, Hyperbola

easy

The equation of the ellipse whose latus rectum is $8$ and whose eccentricity is $\frac{1}{{\sqrt 2 }}$, referred to the principal axes of coordinates, is

A

$\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$

B

$\frac{{{x^2}}}{8} + \frac{{{y^2}}}{9} = 1$

C

$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{32}} = 1$

D

$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{24}} = 1$

Solution

(c) $\frac{{2{b^2}}}{a} = 8,$$e = \frac{1}{{\sqrt 2 }}$

${a^2} = 64,\,{b^2} = 32$

Hence required equation of ellipse is

$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{32}} = 1$.

Standard 11

Mathematics

Share

Similar Questions

If a tangent having slope of $ – \frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to ……………… $\mathrm{sq. \, units}$ ($O$ is centre of the ellipse)

hard

On the ellipse $4{x^2} + 9{y^2} = 1$, the points at which the tangents are parallel to the line $8x = 9y$ are

medium

(IIT-1999)

The locus of the foot of perpendicular drawn from the centre of the ellipse ${x^2} + 3{y^2} = 6$ on any tangent to it is

hard

(JEE MAIN-2014)

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ be an ellipse with foci $F_1$ and $F_2$. Let $AO$ be its semi-minor axis, where $O$ is the centre of the ellipse. The lines $A F_1$ and $A F_2$, when extended, cut the ellipse again at points $B$ and $C$ respectively. Suppose that the $\triangle A B C$ is equilateral. Then, the eccentricity of the ellipse is

normal

(KVPY-2018)

A circle has the same centre as an ellipse and passes through the foci $F_1 \& F_2$ of the ellipse, such that the two curves intersect in $4$ points. Let $'P'$ be any one of their point of intersection. If the major axis of the ellipse is $17 $ and the area of the triangle $PF_1F_2$ is $30$, then the distance between the foci is :

normal