Prove that the straight line x+ y = 1 touches the parabola `y= x-x^2`

Prove that the straight line 5x + 12 y = 9 touches the hyperbola x ^(2) - 9 y ^(2) =9 and find the point of contact.

The straight line x+y= k touches the parabola y=x-x^(2) then k =

Show that the line x + y = 1 touches the parabola y = x-x ^(2).

The straight line x+y touches the parabola y=x-x^(2) then k =

The line x+y=k touches the parabola y=x-x^(2) if k=

Prove that the straight line y = x + a sqrt(2) touches the circle x^(2) + y^(2) - a^(2)=0 Find the point of contact.

Statement I Straight line x+y=lamda touch the parabola y=x-x^2 , if k=1. Statement II Discriminant of (x-1)^2=x-x^2 is zero.

Statement I Straight line x+y=lamda touch the parabola y=x-x^2 , if lamda=1 . Statement II Discriminant of (x-1)^2=x-x^2 is zero.

Statement I Straight line x+y=k touch the parabola y=x-x^2 , if k=1. Statement II Discriminant of (x-1)^2=x-x^2 is zero.