·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

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`