QJEEM11Mac85d: JEE Main 2011 Mathematics - Class 11 JEEM11Mac85d Solution: Equation of the ellipse whose axes of coordinates and which…

Question

Verified Solution • 2025–26 Session moderate

Equation of the ellipse whose axes of coordinates and which passes through the point

(-3,1)

and has eccentricity

\sqrt {{2 \over 5}}

is :

Accepted Answer

Let the ellipse be

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

It press through

(-3, 1)

so

{9 \over {{a^2}}} + {1 \over {{b^2}}} = 1\,\,\,\,\,\,...\left( i \right)

Also,

{b^2} = {a^2}\left( {1 - 2/5} \right)

\Rightarrow 5{b^2} = 3{a^2}\,\,\,\,\,\,\,\,\,...\left( {ii} \right)

Solving

(i)

and

(ii)

we get

{a^2} = {{32} \over 3},{b^2} = {{32} \over 5}

So, the equation of the ellipse is

3{x^2} + 5{y^2} = 32

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