Question

The curve represented by $x=3\cos t+3\sin t$ and $y=4\cos t-4\sin t$ is

• A. An ellipse
• B. A hyperbola
• C. A parabola
• D. None of these

Answer 1

The correct option is A An ellipse

The equations of curve are

$x=3(\cos t+\sin t)$

$\Rightarrow \frac{x}{3}=\cos t+\sin t....\left(i\right)$

and $y=4(\cos t-\sin t)$

$\Rightarrow \frac{y}{4}=(\cos t-\sin t)....\left(ii\right)$

On squaring and adding (i) and (ii)

$\frac{x^2}{9}+\frac{y^2}{16}=2({\sin }^{2}t+{\cos }^{2}t)$

$\Rightarrow \frac{x^2}{9}+\frac{y^2}{16}=2$ Which is an ellipse
Hence choice (a) is correct answer.