JEE MATHEMATICS MCQ: ELLIPSE

1 Medium

1 of 1

Analyzing +4 | -1

If the normals at the points

A, B, C

and

D

of an ellipse meet in a point

O

, then

S A \cdot S B \cdot S C \cdot S D

is equal to (where,

S

is one of the foci)

View answer and explanation

Correct option: A

\frac{b^2}{e^2} \cdot S O^2

Option A (

\frac{b^2}{e^2} \cdot S O^2

) is correct because after substituting and simplifying the expression for the product of distances from the foci to the points, it equals

\frac{b^2}{e^2} \cdot S O^2

More Questions from ELLIPSE

Practice All Chapter MCQs →

\frac{x^2}{144}+\frac{y^2}{81}=1

m

\mathrm{M}

\mathrm{mM}

P

\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1

S

S'.

A

PSS',

A

A

B

(\sqrt{7}, 0)

(-\sqrt{7}, 0)

P

9 x^{2}+16 y^{2}=144

\mathrm{PA}+\mathrm{PB}

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

r

\frac{x^2}{25}+\frac{y^2}{16}=1

P

x=0

Q

R

Q

y=x

Q

R

N P

Q

P

O