Find the equation for the following parabola.
Vertex (2, 3)
Focus (7, 3)

A. (x-3)2 = 20(y-2)
B. (y-3)2 = 20(x-2)
C. (x-2)2 = 20(y-3)
D. (y+3)2 = 20(x+2)

The equation of the parabola is;

(y-3)^2 = 20(x-2)

Step-by-step explanation:

Here, we want to find the equation of the parabola given the focus and the vertex of the said parabola

Mathematically, we can have the equation represented as;

(y-k)^2 = 4a(x-h)

As we can see that the focus and the vertex lie on the same horizontal line of y = 3

In this case, a = 7-2 = 5

The coordinates of the vertex is (h,k) = (2,3) in this case

where h = 2 and k = 3

So the equation of the parabola will be;

(y- 3)^2 = 4(5)(x-2)

(y-3)^2 = 20(x-2)

option (a)

step-by-step explanation:

step 1:   take 2 number whose product equal to 25..

and sum of those two number are -10

step: 2 for example here if we take 5,5 are the number,,

5*5=25

and

5+5=10

but we need -10

so if we take   -5,-5

so -5*-5=25

and -5+(-5)=-10

s0

come the equation

replace -10x by these number

like -5x -5x+25

take common

x(x-5)-5(x-5)=0

(x-5)(x-5)=0

set the two equations for y equal to each other. solve for x. this will be the x-coordinate for the point of intersection. use this x-coordinate and plug it into either of the original equations for the lines and solve for y.