Find the The Slopes of the tangent and the normal to the following curves at the indicated points :

Question

Find the The Slopes of the tangent and the normal to the following curves at the indicated points : x 2 + 3y + y 2 = 5 at (1, 1)

Philoid · Accepted Answer

Given:

x² + 3y + y² = 5 at (1,1)

Here we have to differentiate the above equation with respect to x.

⇒ (x² + 3y + y²) = (5)

⇒ (x²) + (3y) + (y²) = (5)

(xⁿ) = n.x^{n – 1}

⇒ 2x + 3 + 2y = 0

⇒ 2x + (3 + 2y) = 0

⇒ (3 + 2y) = – 2x

⇒

The Slope of the tangent at (1,1)is

⇒

The Slope of the tangent at (1,1) is

⇒ The Slope of the normal =