y2 10y 27 1330 Solutiony2 10y 27x 133 0 Making a perfect squ

Solution

y^2 -10y -27x +133 =0

Making a perfect square on RHS:

y^2 -10y = 27x -133

(y - 5)^2 = 27x -133 +25

( y-5)^2 = 27x - 108

27x = ( y -5)^2 + 108

x = (1/27)( y -5)^2 + 108/27

x = (1/27)( y -5)^2 + 4 ------> sideways parabola that opens to the right.

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

Vertex ( 4, 5)

4p = 27 ---> p = 27/4 = 6.75

Focus : ( 10.75 , 5)

Directrix : x = 10.75 - 6.75 = 4

x =4