If the equation `m^(2)(x + 1) + m(y – 2) + 1 = 0` represents a family of lines, where ‘m’ is parameter then find the equation of the curve to which these lines will always be tangents.

Explanation

`m^(2)(x + 1) + m(y – 2) + 1 = 0`. The equation of the curve to which above lines will always be tangents can be obtained by equating its discriminant to zero.
`therefore(y-2)^(2)-4(x+1)=0`
`!y^(2)-4y+4-4x-4=0`
`!y^(2)=4(x+y)`