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P is a variable point on the line L=0 . ...

P is a variable point on the line `L=0` . Tangents are drawn to the circles `x^(2)+y^(2)=4` from P to touch it at Q and R. The parallelogram PQSR is completed.
If `P -=(3,4)`, then the coordinates of S are

A

`(-46//25,63//25)`

B

`(-51//25,-68//25)`

C

`(-46//25,68//25)`

D

`(-68//25,51//25)`

Text Solution

Verified by Experts

The correct Answer is:
2
As `P -= (3,4)` , the equation of QR is
`3x+4y=4 ` (1)
Let ` S -= (x_(1),y_(1))`.
S is the mirror image of P w.r.t. (1). Then,
`(x_(1)-3)/(3)=(y_(1)-4)/(4)= (-2(3xx3+4xx4-4))/(3^(2)+4^(2))=-(42)/(25)`
`:. x_(1)=-(51)/(25),y_(1)=-(68)/(25)`
or `S-=(-(51)/(25),-(68)/(25))`
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