Question

The value of the diameter of the circle guided by the equations:

$x=3\cos \theta +4\sin \theta$ and

$y=4\cos \theta -3\sin \theta$ is equal to:

Answer 1

$x=3\cos \theta +4\sin \theta y=4\cos \theta -3\sin \theta x^2+y^2=9{\cos }^2\theta +16{\sin }^2\theta +12.2\sin \theta \cos \theta +16{\cos }^2\theta +9{\sin }^2\theta -12.2\sin \theta \cos \theta x^2+y^2=25({\sin }^2\theta +{\cos }^2\theta )x^2+y^2=5^2$
Diameter$=2\times r=2\times 5=10$