Find (dy)/(dx \: ) of \: \frac{x {}^(2) }{a {}^(2) } + \frac{y {}^(2) }{b { }^(2) } = 1 \\ \\ if \: x = a \cos( \alpha \:) \: and \: \: y \: = b \sin( \alpha ) pls help me ​

Question

Find


`(dy)/(dx \: ) of \: \frac{x {}^(2) }{a {}^(2) } + \frac{y {}^(2) }{b { }^(2) } = 1 \\ \\ if \: x = a \cos( \alpha \:) \: and \: \: y \: = b \sin( \alpha )`
pls help me ​

Answer 1

dy/dx = -b/a cot α

Explanation:

x² / a² + y² / b² = 1

Take derivative with respect to x.

2x / a² + 2y / b² dy/dx = 0

2y / b² dy/dx = -2x / a²

dy/dx = -b²x / (a²y)

Substitute:

dy/dx = -b²a cos α / (a²b sin α)

dy/dx = -b cos α / (a sin α)

dy/dx = -b/a cot α