The normal to a given curve at each point `(x ,y)` on the curve passes through the point `(3,0)dot` If the curve contains the point `(3,4),` find its equation.

Explanation

Let P(x, y) be any point on the curve. The equation of the normal at P(x, y) to the given curve is given as `Y-y=-frac{1}{frac{d y}{d x}}(X-x)`

It is given that the curve passes through the point (3,0). Then,
`


0-y=-frac{1}{frac{d y}{d x}}(3-x) `
`
Rightarrow-y=-frac{1}{frac{d y}{d x}}(3-x) `
`
Rightarrow y frac{d y}{d x}=3-x `
`
Rightarrow y d y=(3-x) d x `
`
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