Question

if x =a cos theta ,y=b sin theta , then find (b²x²+a²y²) ​

Answer 1

Value: 0

Work 1:

Given, x = a cos theta and y = b sin theta. Substituting for x and y ,

b²x² + a²y² - a²b² = b²a² cos² theta + a²b² sin² theta - a²b²

= a²b² (cos² theta + sin² theta) - a²b²

= a²b² . 1 - a²b² (Using the trigonometric identity cos² theta + sin² theta = 1)

= a²b² - a²b² = 0 (Proved)

Work 2:

x = a cos theta , y = b sin theta . Substituting for x,

b²x² + a²y² - a²b² = b²a² cos² theta - a²b² + a²y²

= b²a²(cos² theta-1) + a²y²

= b²a²(-sin² theta) + a²y² = -a²(b²sin² theta) + a²y² Substitute y for b sin theta.

=-a²y² + a²y²

= 0 (Proved)
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