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Question

The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point $$(4,3)$$. The equation of the curve is


A
x2=y+5
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B
y2=x5
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C
y2=x+5
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D
x2=y5
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Solution

The correct option is B $${ y }^{ 2 }=x+5$$
According to the question, we have 
$$\cfrac { dy }{ dx } =\cfrac { 1 }{ 2y } $$
$$\Rightarrow 2ydy=dx$$
On integrating, we get
$${ y }^{ 2 }=x+C$$
This passes through $$(4,3)$$
Therefore, $$  9=4+C\Rightarrow C=5$$
Hence,, the equation of the curve is $${ y }^{ 2 }=x+5$$.

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