The curve with parametric equations $x = \alpha + 5\cos{ heta,}\ y = \beta + 4\sin heta$ (where $ heta$ is parameter) is

Question

The curve with parametric equations $x = \alpha + 5\cos{	heta,}\ y = \beta + 4\sin	heta$ (where $	heta$ is parameter) is

Dr. Abubacker · Accepted Answer

(b)
Given equation of curve is $x = \alpha + 5\cos{	heta,}\ y = \beta + 4\sin	heta$
Or $\cos	heta = \frac{x - \alpha}{5},\sin	heta = \frac{y - \beta}{4}$
$\because\cos^{2}	heta + \sin^{2}	heta = 1$
$\Rightarrow \left( \frac{x - \alpha}{5} ight)^{2} + \left( \frac{y - \beta}{4} ight)^{2} = 1$
This represents the equation of an ellipse.

Q. The curve with parametric equations $x = \alpha + 5\cos{\theta,}\ y = \beta + 4\sin\theta$ (where $\theta$ is parameter) is

Explanation

Reviewed by Dr. Abubacker

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