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Question

Find the vertex, axis, focus, directrix, latus rectum of the parabola 4y2+12x20y+67=0.

A
Vertex : (72,52), Axis : y=52, Focus : (174,52), Directrix :x=114; LR =3
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B
Vertex : (92,52), Axis : y=52, Focus : (174,52), Directrix :x=114; LR =4
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C
Vertex : (92,52), Axis : y=52, Focus : (174,52), Directrix :x=114; LR =3
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D
Vertex : (72,52), Axis : y=52, Focus : (174,52), Directrix :x=114; LR =4
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Solution

The correct option is A Vertex : (72,52), Axis : y=52, Focus : (174,52), Directrix :x=114; LR =3
Consider, 4y2+12x20y+67=0
4(y25y)=12x67
4(y22.52y+5222)=12x67+25=12x42
(y52)2=3(x+72)
Vertex :(72,52),

Axis :y=52
Focus :(7234,52)=(174,52)
Directrix :x+72=34x=114
And Latus rectum =4×34=3

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