Question

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

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

Answer 1

The correct option is A an ellipse

Given $x=3(\cot t+\sin t),y=4(\cos t-\sin t)$

From the given relation, we have ${\left(\frac{x}{3}\right)}^2+{\left(\frac{y}{4}\right)}^2={(\cos t+\sin t)}^2+{(\cos t-\sin t)}^2$

$\Rightarrow \frac{x^2}{9}+\frac{y^2}{16}=2$

$\Rightarrow \frac{x^2}{18}+\frac{y^2}{32}=1$

which is an ellipse.