If the normals of the parabola `y^(2)=4x` drawn at the end points of its latus rectum are tangents to the circle `(x-3)^(2)+(y+2)^(2)=r^(2)` then the value of `r^(2)` is _________.

Options

A. 4
B. 2
C. 6
D. 9

Answer

B

Explanation

The coordinates of end-points of latusrectum PQ of the parabola `y^(2)=4x` are P(1, 2) and Q(1, -2). The equations of the normals P and Q are
`y-2=-2/3(x-1)`
and `y+2=-(-2)/2(x-1)" "["Using "y-y_(1)=(y_(1))/(2a)(x-x_(1))]`
or `x+y-3=0 and x-y-3=0`
These are tangents to teh circle `(x-3)^(2)+(y+2)^(2)=r^(2)`
`:." "|(3-2-3)/(sqrt(1^(2)+1^(2)))|=rrArrr=sqrt2rArrr^(2)=2`.