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If the circle `x^2+y^2+2gx+2fy+c=0`is touched by `y=x`at `P`such that `O P=6sqrt(2),`then the value of `c`is36 (b) 144(c) 72 (d)none of theseA. 36B. 144C. 72D. none of these |
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Answer» Correct Answer - 3 The equation of the line `y=x` in distance form is `(x)/(cos theta)=(y)/(sin theta)=r`, where ` theta =(pi)/(4)` For point P`, r=6 sqrt(2)`. Therefore, the coordinates of P are given by `(x)/(cos (pi//4))=(y)/(sin (pi//4))=6 sqrt(2)` or `x=6,y=6` Since `y=x` touches the circle, the equation `2x^(2)+2x(g+f)+c=0` has the equal roots . Therefore, `4(g+f)^(2)=8c` or `(g+f)^(2)=2c` (2) From (1), we get `[12(g+f)^(2)=[-(c+72)]^(2)` or `144(g+f)^(2)=(c+72)` or`144(2c)=(c+72)^(2)` or `(c-72)^(2)=0` or `c=72` |
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