A line passing through the point $P(\sqrt{5}, \sqrt{5})$ intersects the ellipse $\frac{x^2}{36} + \frac{y^2}{25} = 1$ at $A$ and $B$ such that $(PA)\cdot(PB)$ is maximum. Then $5(PA^2 + PB^2)$ is equal to :

JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q12

Question 12 of 75 in this shift, Maths question 12 of 25, Section A.

A line passing through the point

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

intersects the ellipse

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

A

and

B

such that

(PA)\cdot(PB)

is maximum. Then

5(PA^2 + PB^2)

is equal to :

Official answer

Option 3

NTA final key.