Question

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

• A. ellipse
• B. parabola
• C. hyperbola
• D. circle

Answer 1

Answer: (A)

Given relations are
$x=3(\cos t+\sin t),y=4(\cos t-\sin t)$
$\Rightarrow \frac{x}{3}=\cos t+\sin t,\frac{y}{4}=\text{cos t}-\sin t$
$\Rightarrow {\left(\frac{x}{3}\right)}^2+{\left(\frac{y}{4}\right)}^2=(\cos t+\sin t{)}^2$
$+(\cos t-\sin t{)}^2$
$\Rightarrow \frac{x^2}{9}+\frac{y^2}{16}=2$
$\Rightarrow \frac{x^2}{18}+\frac{y^2}{32}=1$, which is an ellipse.