For the parabola $y^{2} + 8 x - 12 y + 20 = 0$

Vertex is

(2, 6)

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Focus is

(0.6)

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Latusrectum

4

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Axis

y = 6

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Solution

The correct options are
A Vertex is $(2, 6)$
C Focus is $(0.6)$
D Axis $y = 6$
Given parabola can be rewritten as
${(y - 6)}^{2} = - 8 (x - 2)$
Which is of the form
$Y^{2} = - 4 A X$
Where $Y = y - 6, X = x - 2, A = 2$
$∴$ Vertex $(2.6)$
Focus $(0.6)$
Latusrectum $= 4 A = 4 \times 8$
Axis is $y = 6$

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For the parabola y2+8x−12y+20=0

The correct options are A Vertex is (2,6) C Focus is (0.6) D Axis y=6Given parabola can be rewritten as(y−6)2=−8(x−2)Which is of the formY2=−4AXWhere Y=y−6,X=x−2,A=2∴ Vertex (2.6)Focus (0.6)Latusrectum=4A=4×8Axis is y=6

For the parabola $y^{2} + 8 x - 12 y + 20 = 0$