A line passing through the point P(√(5),√(5)) intersects the ellipse (x²)/36+(y²)/25=1 at points A and B such that (PA)·(PB) is maximum. Then 5 (PA²+PB²) is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q81

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

A line passing through the point

P(\sqrt{5},\sqrt{5})

intersects the ellipse

\dfrac{x^2}{36}+\dfrac{y^2}{25}=1

at points

A

and

B

such that

(PA)\cdot(PB)

is maximum. Then

5\bigl(PA^2+PB^2\bigr)

is equal to: