Question

# A parabola has its vertex at the origin; its axis lies along the x-axis and it passes through the point $$P(2,3)$$. The equation of the parabola is

A
4y2=9x
B
y2=49x
C
y2=92x
D
y2=32x

Solution

## The correct option is C $${ y }^{ 2 }=\cfrac { 9 }{ 2 } x$$The vertex of the parabola is $$O(0,0)$$ and tis axis lie along the x-axis. So its equation is $${ y }^{ 2 }=4ax\quad or\quad { y }^{ 2 }=-4ax$$But it passes through the point $$P(2,3)$$ so its equation is $${ y }^{ 2 }=4ax$$since it passes through $$P(2,3)$$ we have $$4a\times 2=9\Rightarrow a=\cfrac { 9 }{ 8 }$$its equation is $${ y }^{ 2 }=4\times \cfrac { 9 }{ 8 } x\Rightarrow { y }^{ 2 }=\cfrac { 9 }{ 2 } x\quad$$Mathematics

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