If the normals of the paralbola 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

Answer

2

Explanation

2 End point of latus rectum of parabola `y^(2)=4x` are `(1,pm2)`.
Equation of normals at points `(1,pm2)` are
y=-+3 and y=x-3
`orx+y-3=0andx-y-3=0`
These lines are tangent to circle, `(x-3)^(2)+(y+2)^(2)=r^(2)`
`:." "|(3pm2-3)/(sqrt(1+2))|=r`
`or" "r^(2)=2`