If x = a cos θ and y = b sin θ, then the value of b²x² + a²y² is:
Correct: A
Given x = a cos θ, we can write cos θ = x/a.
Given y = b sin θ, we can write sin θ = y/b.
We know the fundamental trigonometric identity: sin² θ + cos² θ = 1.
Substitute the expressions for sin θ and cos θ into the identity:
(y/b)² + (x/a)² = 1
y²/b² + x²/a² = 1
To combine the terms on the left side, find a common denominator (a²b²):
(a²y² + b²x²) / (a²b²) = 1
Multiply both sides by a²b²:
a²y² + b²x² = a²b².