Tangent are drawn to the circle `x^2+y^2=1` at the points where it is met by the circles `x^2+y^2-(lambda+6)x+(8-2lambda)y-3=0,lambda` being the variable. The locus of the point of intersection of these tangents is (a) `2x-y+10=0` (b) `2x+y-10=0` (c) `x-2y+10=0` (d) `2x+y-10=0`

Explanation

Point of intersection of these tangents will be common chord of contact.

Let coordinates of common chord of contact is `(h,k)`.

So, equation of chord of contact can be given by,

`hx+ky = 1` `->` Eq(1)

Bow, other way of writinf equation for common chord of contact is

`S1-S2=0`

So, subtracting equations of given circles,

`x^2+y^2-x^2-y^2+(lambda+6)x-(8-2lambda)y+3=1`

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