Question

p1 is a parabola of y^2=4x and p2 is parabola given by y^2=4b(x+a).p2 passes through a and b which are the points of intersection of p1 and line x=a .if t is the point of intersection of tangent to p1 and a and b ,and r is the point of intersection of normal at a and b to p2 the area of quadrilateral tarb is​

Answer 1

∵ Length of tangents from a point to circle are equal.

PQ=PR

Then parallelogram PQRS is rhombus.

∴ Mid-point of QR= midpoint of PS

and QR⊥PS

∴S is the mirror image of P w.r.t. QR

∵L≡2x+y=6

Let P≡(λ,6−2λ)

∵∠PQO=∠PRO=2π

∴OP is diameter of circumcircle PQR then centre is 

(2λ,3−λ)

∴x=2λ⇒λ=2x

and y=3−λ,

then 2x+y=3∵P≡(2,3)

∴ Equation of QR is 2x+3y=4

Let S≡(α,β)

⇒2α−2=3β−3=(4+9)−2(4+9−4)=13−18

∴α=−1310,β=