If the line `k^(2)(x-1)+k(y-2)+1=0` touches the parabola `y^(2)-4x-4y+8=0`, then k can be

Options

A. -3
B. `-sqrt(5)`
C. `(7)/(19)`
D. 1000

Answer

A, B, C, D

Explanation

1,2,3,4
Given parabola is
`(y-2)^(2)=4(x-1)`
Equation of tangent having slope m is
`(y-2)=m(x-1)+(1)/(m)`
`orm^(2)(x-1)-m(y-2)+1=0`
`or(-m)^(2)(x-1)+(-m)(y-2)+1=0`
Comparing with given equation of tangent,
`kinR-{0}`