need help!!!!HELP!!?

Question

find the vertex, focus, ends of latus rectum, and the directrix, (y+3/2)2=2(x-5/2)...number 2 is an exponent...not the no. 2 inside the parenthesis...

Answer 1

(y+1.5)² = 2(x-2.5)
This is an equation of parabola opened to the right.

For understanding the problem I recommend you to look here:
http://mathworld.wolfram.com/Parabola.html
http://mathworld.wolfram.com/LatusRectum.html

Generally, equation of such kind of parabola is
(y - y₀)² = 4 a (x - x₀)
where
(x₀, y₀) - coordinates of the vertex
4 a – latus rectum
a – distance focus to vertex

Now comparing the general equation with parameters of our parabola we get these results:

Vertex is (2.5, -1.5)
Latus rectum is 2
a = 0.5
Focus is (3, -1.5)
The equation of directrix is x = 2
End points of latus rectum are (3, -0.5) and (3, -2.5).

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