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

Question

Philoid · Accepted Answer

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)

∴