Verified Solution • 2025–26 Session moderate

QJEEM19Ma7e8c: JEE Main 2019 Mathematics - Class 11 JEEM19Ma7e8c Solution: Let the length of the latus rectum of an ellipse with its major …

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

Multiple Choice Options

A $\left( {4\sqrt 2 ,2\sqrt 3 } \right)$
B $\left( {4\sqrt 3 ,2\sqrt 3 } \right)$
C $\left( {4\sqrt 3 ,2\sqrt 2 } \right)$
D $\left( {4\sqrt 2 ,2\sqrt 2 } \right)$

Step-by-Step Verified Solution

{{2{b^2}} \over a} = 8

and 2ae

=

\Rightarrow

{b \over a}

= e and 1

-

e² = e²

\Rightarrow

=

{1 \over {\sqrt 2 }}

\Rightarrow

b = 4

\sqrt 2

and a

=

8

So equation of ellipse is

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

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