P is a variable point on the line L=0. Tangents are drawn to the circle x2+y2=4 from P to touch it at Q and R. The parallelogram PQRS is completed.
If P≡(3,4), then coordinate of S is
A
(−4625,−6325)
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B
(−5125,−6825)
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C
(−4625,−6825)
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D
(−6825,−5125)
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Solution
The correct option is B(−5125,−6825)
∵P≡(3,4) ∴ Equation of QR is T=0⇒3x+4y=4…(1) Let S≡(x1,y1) ∵S is the mirror image of P w.r.t equation(1), then x1−33=y1−44=−2(3×3+4×4−4)32+42=−4225 ∴x1=−5125,y1=−6825⇒S≡(−5125,−6825)