Question

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Answer 1

Answer:

The answer is a² .

Step-by-step explanation:

You have to substitute x and y into the expression :

$let \: x = a \cos(θ) \\ let \: y = a \sin( θ)$

${x}^{2} + {y}^{2} = {(a \cosθ )}^{2} + {(a \sinθ) }^{2}$

${x}^{2} + {y}^{2} = {a}^{2}( {cos}^{2}θ) + {a}^{2} ({sin}^{2}θ)$

Next, you have to apply Basic Trigonometric Identity :

${sin}^{2} θ + {cos}^{2} θ = 1$

${x}^{2} + {y}^{2} = {a}^{2} ( {cos}^{2} θ + {sin}^{2} θ)$

${x}^{2} + {y}^{2} = {a}^{2} (1)$

${x}^{2} + {y}^{2} = { a}^{2}$