Question

derive the equation of the parabola with a focus at (4,-7) and a directrix of y=-15. put the equatiom in standard form

Answer 1

the parabola is concave up because the directrix is below the focus

find the distance between the focus and directrix





the focal length is the distance between the focus and the vertex, can be represented by the letter a.

when you have the value of 2a, halve it to find a.

the vertex will be on x = 4 and a units below the focus.

when you have the vertex and focal length the equation will be

\[(x - h)^2 = 4\times a \times(y - k)\]

where (h, k) is the vertex and a is the focal length