Let S and S’ be the foci of an ellipse and B be any one of the extremities of its minor axis. If $Δ S' B S$ is a right angled triangle with right angle at B and area $(Δ S' B S) = 8 s q$ . Units, then $S_{1} :$ Length of a latus of a latus rectum of the ellipse is 4 units
$S_{2} :$ Distance between foci is $4 \sqrt{2}$ units.
$S_{3} :$ Length of the minor axes is 8 units
Then the number of statements which are false is:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$Δ S' B S$ is right angled triangle, then
(Slope of $B S$ ) $\times$ (Slope of $B S'$ ) $= - 1$
Question Image
$\frac{b}{- a e} \times \frac{b}{a e} = - 1 \Rightarrow b^{2} = a^{2} e^{2}$ ……………. (i)
Since, area of $Δ S' B S = 8$
$\Rightarrow \frac{1}{2} .2 a e . b = 8 \Rightarrow b^{2} = 8$ …………… (ii)
From eqn (i), $a^{2} e^{2} = 8$
Also, $e^{2} = 1 - \frac{b^{2}}{a^{2}}$
$\Rightarrow a^{2} e^{2} = a^{2} - b^{2} \Rightarrow 8 = a^{2} - 8 \Rightarrow a^{2} = 16$
Hence, required length of latus rectum
$= \frac{2 b^{2}}{a} = \frac{2 (8)}{4} = 4$ units.