Thread: maths - parabola

The equation of a parabola is given by x^2 - 4x - 2y + 8 = 0
find the vertex, the focus and the equation of the normal to the parabola at the point (0,4)

Originally Posted by deej813

The equation of a parabola is given by x^2 - 4x - 2y + 8 = 0
find the vertex, the focus and the equation of the normal to the parabola at the point (0,4)

Transform the given equation into the form

by completing the square.

Then the vertex is at V(k, h).

The focus is at F(k, h+p)

Calculate the slope of the tangent at (0, 4) and afterwards calculate the perpendicular direction.