Question

P is a variable point of the line L = 0. Tangents are drawn to the circle x2 + y = 4 from P to touch it at Q and R. The parallelogram PQSR is completed,
14. If P = (3, 4). then coordinate of S 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=

Answer 2

Area of square is 169cm2.

Let a be side of square.

Area = a2=169

a2=(13)2

[a=13 cm.]

side of square is 13 cm