Question

Need help with this question: Write the equation of the parabola with focus (5,2) and directrix x=1

Answer 1

Directrix is x =1, so it is horizontal parabola.Vertex is between the focus and directrix on equal distance 5-x=x-1, 2x=6,
x=3. y -coordinate of the vertex for this parabola equals y-coordinate of the focus.
Vertex (3,2).

Focus has x=5 >1, so it is directed to the right.
`(y-y_(0))^(2)=4p(x-x_(0)) \\(y-2)^(2)=4p (x-3) p is a distance between vertex and focus, and equals abs(p)=abs(5-3)= 2 \\(y-2)^(2)=(4*2) (x-3) \\(y-2)^(2)= 8 (x-3)`