Conic Sections Question 308

Question: The curve represented by $ x=2(cost+sint),,y=5(cost-sint) $ is

Options:

A) A circle

B) A parabola

C) An ellipse

D) A hyperbola

Show Answer

Answer:

Correct Answer: C

Solution:

[c] $ x=2\cos t+sint $

$ y=5(cost-sint)\Rightarrow \frac{x^{2}}{4}+\frac{y^{2}}{25}=2\Rightarrow $ Ellipse