Question

The locus of extremities of the latus rectum of the family of ellipse $b^2{x}^2+y^2=a^2{b}^2$ is

• A. $x^2-ay=a^2$
• B. $x^2-ay=b^2$
• C. $x^2+ay=a^2$
• D. $x^2+ay=b^2$

Answer 1

Answer: (A), (C)

The correct options are
A $x^2-ay=a^2$
C $x^2+ay=a^2$

Exterrmities of the latus recturn

$=(\pm ae,\pm \frac{a^2{b}^2}{a})$

$\therefore K=\pm a{b}^2$

$h=\pm a\sqrt{1-b^2}$

$\Rightarrow h^2=a^2-\left(a^2{b}^2\right)$

$\Rightarrow h^2+a\left(a{b}^2\right)=a^2$

$\Rightarrow h^2\pm ak=a^2$

$\Rightarrow x^2\pm ay=a^2$