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

Question

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

Answer 1

Given the slope of the tangent = \(-\frac{x}{y}\)

We know that slope of tangent = \(\frac{dy}{dx}\)

Integrating both sides,

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

So, it must satisfy the above equation

Putting the value of c1 in equation (1)

∴ y² + x² = 25