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Question

# Find the vertex, axis, focus, directrix, latus rectum of the parabola 4y2+12xâˆ’20y+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 =3Consider, 4y2+12x−20y+67=04(y2−5y)=−12x−674(y2−2.52y+5222)=−12x−67+25=−12x−42(y−52)2=−3(x+72)⇒ Vertex :(−72,52), Axis :y=52 Focus :(−72−34,52)=(−174,52)Directrix :x+72=34⇒x=−114 And Latus rectum =4×34=3

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