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 $\frac{x}{3}=\cos t+\sin t\&\frac{y}{4}=\cos t-\sin t$
Squaring these two,
$\Rightarrow \frac{x^2}{9}=1+2\cos t\sin t$.........(i)
$\frac{y^2}{16}=1-2\sin t\cos t$........(ii)
Adding (i) & (ii)
$\frac{x^2}{9}+\frac{y^2}{16}=2\Rightarrow \frac{x^2}{18}+\frac{y^2}{32}=1$