JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q11

← JEE Main 2022 · 27 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 11 of 90

Let $P(a,b)$ be a point on the parabola $y^2=8x$ such that the tangent at P passes through the centre of the circle $x^2+y^2-10x-14y+65=0$ . Let A be the product of all possible values of $a$ and B be the product of all possible values of $b$ . Then the value of $A+B$ is equal to

Answer and worked solution

Official answer: D

Tangent at $(2t^2,4t)$ : $ty=x+2t^2$ . Through the centre $(5,7)$ : $2t^2-7t+5=0$ , so $t=1$ or $\frac52$ .

Points $(2,4)$ and $\left(\frac{25}2,10\right)$ : $A=25$ , $B=40$ .

$A+B=65$ . (D)

Topics:Tangents and normals to conics Parabola Equation of a circle

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 11