Question

Write the equation for a parabola with a focus at (-2,5) and a directrix at y=3.

Answer 1

Answer:

(x+2)²=4(y-4)

or y=1/4 (x+2)²+4

Step-by-step explanation:

directrix y=3 and focus (-2,5) to find te equation of parabola we use the equation :

(x-h)²=4p(y-k)

vertex(h,k) : the vertex is half way between the focus and the directrix

y(vertex)=y(focus)+directrix/2

y=5+3/2 ⇒8/2=4

x is the same as the c of the focus =-2

vertex (-2,4)

to find the distance (p) which is the distance between the vertex and focus

p=5-4=1

substitute h=(-2), k=(4) and p=(1) in the equation : (x-h)²=4p(y-k)

(x-(-2)²=4(1)(y-4)

(x+2)²=4(y-4)