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)
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
$\displaystyle 4p(y-h)=(x-k)^2$ 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.