Find parametric equations for the rectangular equation x^2 + y^2 – 25 = 0.?
A) x = cos 5t, y = sin 5t, 0 ≤ t ≤ 2π
B) x = cos t, y = 5 sin t, 0 ≤ t ≤ 2π
C) x = 5 cos t, y = sin t, 0 ≤ t ≤ 2π
D) x = 5 cos t, y = 5 sin t, 0 ≤ t ≤ 2π
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the answer is option (d).
x^2 + y^2 =25
this is the equation of a circle with centre origin and radius 5
so wen u substitute the co-ordinates of (d) u get the above quation,
25cos^2t + 25sin^2t =25 (since cos^2t + sin^2 t =1)