Q21 of 462 Page 22

Find the equation of the curve which passes through the point (3, – 4) and has the slope at any point (x, y) on it.

Given the slope of the tangent =

We know that slope of tangent =


∴


⇒


Integrating both sides,


⇒


⇒


⇒……(1)


Now, the curve passes through (3, – 4)


So, it must satisfy the above equation


∴


⇒ – 4 = (3)2× c


⇒ – 4 = 9c


⇒ c =


Putting the value of c in equation (1)


∴


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