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
B
y2=x5
C
y2=x+5
D
x2=y5

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 $${ y }^{ 2 }=x+5$$.Maths

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