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 `2x-y+10=0` (b) `2x+y-10=0` `x-2y+10=0` (d) `2x+y-10=0`

Options

A. `2x-y+10=0`
B. `x+2y-10=0`
C. `x-2y+10=0`
D. `2x+y-10=0`

Answer

1

Explanation

Equation of common chord of the circles is
`-1+(lambda+6)x-(8-2lambda)y+3=0`
or `(lambda+6)x-(8-2lambda)y+2=0` (2)
Let the tangents at the extremities of common chord intersetc at P(h,k).
Thus, equation of chord of contact of circle `x^(2)+y^(2)=1` w.r.t. point P is
`hx+k=1` (2)
Equations (1) and (2) represent the same straight line.
`:. (h)/(lambda+6)=(k)/(2lambda-8)=(-1)/(2)`
Eliminating `lambda`, we get
`2h-k+10=0`
or `2x-y+10=0`