Write the equation of the parabola

1.Vertex(2,5) Focus(2,-3)
2.Directrix=x=3/4 Focus(5/4,-3)

For 1. i got(x-2)^2=32(y-5)^2
For 2. i got y=8x^2-20x-61/60

3 answers

And write the equation of the ellipse
Foci(3,1)and(7,1)
Major axis length=10
I got (x-5)^2/5+(y-1)^2/0=1
as a quick check, go to wolframalpha.com and type in

parabola 8x^2-20x-61/60

It will graph it and describe its properties. Same for the ellipse.

As for #1, you must see that it cannot be a parabola. Not with both x^2 and y^2.
That is not a parabola!
(y-k) should not be squared

should be upside down parabola, sheds water
form

(x-h)^2 = 4 a (y-k)
(x-2)^2 = 4a (y-5)
a = vertex to focus = 8
(x-2)^2 = -32(y-5)
- 32 because sheds water. as x gets big, y goes to - infinity