First slide

Parabola

Question

For the parabola $y^{2} + 8 x - 12 y + 20 = 0$ which of
the following in not correct

Moderate

A

vertex (2, 6)
B

focus (0, 6)
C

length of the latus rectum = 4
D

axis is y = 6

Solution

$(y - 6)^{2} = - 8 (x - 2) or Y^{2} = 4 A X$ where $Y = y - 6$
$X = x - 2, A = - 2,$ vertex is $(2, 6),$ focus is $(X = A, Y = 0)$
i.e., (0, 6) axis is $Y = 0$ i.e. $y = 6$ .and length of the
latus rectum $= | 4 A | = 8$ .

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