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The point of which the line 9x + y - 28 ...

The point of which the line `9x + y - 28 = 0` is the chord of contact of the circle `2x^2+2y^2-3x+5y-7=0` is

Text Solution

Verified by Experts

The correct Answer is:
`(3,-1)`
Let point P be (h,k).
Equation of chord of contact of the given circle w.r.t. point P is
`4hx+4ky-3(x+h)+5(y+k)-14=0`
or `(4h-3)x+(4k+5)y-3h+5k-14=0` (1)
But the given equation of chord of contact is
`9x+y-28=0` (2)
`:. ` Comparing the ratio of coefficients of equation (1) and (2) we get
`(4h-3)/(9) =(4k+5)/(1)=(3h-5k+14)/(28)`
Solving we get `h=3` and `k= -1`.
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