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Match the following lists. |
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Answer» Correct Answer - `a rarr r; b rarr s; c rarr q; d rarr q` a. Since `(2,3)` lies inside the circle, such chord is bisected at (2,3) , which has equation `y-3 = -x(x-2)` or `x+y-5=0` or `a=b=1` b. Let P be the point `(alpha, beta)`. Then `alpha^(2)+beta^(2)+2alpha +2beta =0` The midpoint of OP is `( alpha //2, beta//2)` . Therefore, the locus of `(alpha //2 , beta//2)` is `4x^(2)+4y^(2)+4x+4y=0` i.e., `2g=1,2f=1` and `g+f=1` c. The centes of the circles are (1,2) and (5,-6) The equation of `C_(1)C_(2)` is `y-2= - (8)/(4) (x-1)` i.e., `2x+y-4=0` The equation of the radical axis is `8x-16y-56=0` i.e., `x-2y-7=0` The point of intersection is `(3,-2)`. d. If `theta` is the angle between the tangents, then `(theta)/(2) =("Radius")/("Distance between "(3sqrt(3),3)"and"(0,0))=(1)/(2)` or `(theta)/(2)=(pi)/(6)` or `theta=(pi)/(3)`or `2sqrt(3) tan theta=6` |
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