Verified answer

2y² - 15x - 4y - 28 = 0

Put the equation into vertex form.

regroup terms

15x = 2y² - 4y - 28

factor out leading coefficient

15x = 2(y² - 2y) - 28

divide both sides by the coefficient of x

x = (2/15)(y² - 2y) - 28/15

complete the square

x = (2/15)(y² - 2y + 1²) - (2/15)1² - 28/15

x = (2/15)(y - 1)² - 2

vertex (-2, 1)

p = 1/(4(2/15)) = 15/8

focus (-2+p, 1) = (-1/8, 1)

endpoints of latus rectum: (-0.130, -2.8) and (-1.130, 4.75)

length of latus recturm = 7.5