find the focus of the parabola y=5(x+2)^2+7?

Answer 1

Shift the origin to x= -2 ,y = 7

Put X= x+2 , Y= y-7

Y = 5X²

Comparing to y= 4ax²

4a=5

a = 5/4

Focus in new XY coordinate axes is (0,a)

i.e. X = 0 and Y = 5/4

x+2 = 0 and y-7 = 5/4

x = -2 and y = 33/4

The focus of the parabola y=5(x+2)^2+7 is (-2,33/4)