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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
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B
y2=49x
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C
y2=92x
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D
y2=32x
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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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