Locus: tangent and normal (1 Viewer)

[Jkitty]

Hello,

Please help
10. Find the equation of the tangent to the curve x^2=-2y at the tangent point (4,-8). This tangent meets the directrix at point M. find the coordinates

Thank you

P.s. I got the equation for the tangent I don't know how to find the directrix

 

[matchalolz]

remember that x^2 = -4ay for a negative parabola with vertex at the origin, so in your case:
4a = 2, therefore, a = 1/2

basically a is the focal length, and since your parabola is concave down, the directrix is y = 1/2

then blah blah simultaneous equation to find M?