Question

Eliminate the parameter in the equations x = 5cos(t) – 7 and y = 5sin(t) 9. how can the rectangular equation be described?

Answer 1

Recall that for all t,

cos²(t) + sin²(t) = 1

Now,

x = 5 cos(t) - 7   ⇒   (x + 7)/5 = cos(t)

y = 5 sin(t) + 9   ⇒   (y - 9)/5 = sin(t)

so that substituting into the identity above, we get

((x + 7)/5)² + ((y - 9)/5)² = 1

which we can rewrite as

(x + 7)²/25 + (y - 9)²/25 = 1

(x + 7)² + (y - 9)² = 25

and this is the equation of a circle centered at (-7, 9) with radius 5.