1.

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

Answer»

`(-46//25,63//25)`
`(-51//25,-68//25)`
`(-46//25,68//25)`
`(-68//25,51//25)`

SOLUTION :As `P -=(3,4)` , the equationof QR is
`3x+4y=4 `(1)
Let ` S -= (x_(1),y_(1))`.
S is the MIRROR image of Pw.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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