Equation of the tangent to the circle ,at the point ( 1,-1) ,whose centre is the point of intersection of the straight lines `x-y1`& ` 2 x+ y =3`is `:`

Options

A. 3x-y-4=0
B. x+4y+3=0
C. x-3y-4=0
D. 4x+y-3=0

Answer

B

Explanation

Given lines x-y-1=0 and 2x+y-3=0 intersect at C(4/3, 1/3). The equation of the circle passing through P(1, -1) and having centre at C(4/3, 1/3), is
`(x-(4)/(3))^(2)+(y-(1)/(3))^(2)=(1-(4)/(3))^(2)+(-1-(1)/(3))^(2)`
or, `x^(2)+y^(2)-(8)/(3)x-(2)/(3)y=0`
The equation of the tangent to this circle at (1, -1), is
`x-y-(4)/(3)(x+1)-(1)/(3)(y+1)=0` or, `x+4y+3=0`