The slope of the tangent at a point P(x, y) on a curve is If the curve passes through the point (3, – 4), find the equation of the curve.

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)² + (3)² = c1

⇒ 16 + 9 = c1

⇒ c1 = 25

Putting the value of c1 in equation (1)

∴