parabola pls help.?

Question

A line touches a circle X^2+Y^2=2, and the parabola Y^2=8X. show that its equation is Y=X+2

Answer 1

Using y = x + 2 in the equation of the circle, we find that the line hits the circle when x = -1 and y = 1, so at the point (-1,1).

Similarly, using y = x + 2 in the equation of the parabola, we find x = 2, so y = 4. Thus, the line hits the parabola at (2,4).