Mathematics
If x = h + a cos θ and y = k + a sin θ, prove that (x - h)2 + (y - k)2 = a2.
Trigonometric Identities
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Answer
Given, x = h + a cos θ and y = k + a sin θ
∴ (x - h)2 + (y - k)2 = (h + a cos θ - h)2 + (k + a sin θ - k)2
⇒ (x - h)2 + (y - k)2 = (a cos θ)2 + (a sin θ)2
⇒ (x - h)2 + (y - k)2 = a2 cos2 θ + a2 sin2 θ
⇒ (x - h)2 + (y - k)2 = a2 (cos2 θ + sin2 θ)
⇒ (x - h)2 + (y - k)2 = a2.
Hence, proved that (x - h)2 + (y - k)2 = a2.
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