Question

What are the coordinates of the center and length of radius of a circle whose equation is x^2+y^2-2axcostheta-2aysintheta=0​

Answer 1

Answer:

Step-by-step explanation:

The given equation of the circle is

$\rm{{x}^{2}+{y}^{2}-2ax\cos(\theta)-2ay\sin(\theta)=0}$

Here,

$\sf{g=-a\cos(\theta)\,\,\,\,\,\&\,\,\,\,\,f=-a\sin(\theta)}$

So, the coordinates of the center of the circle ≡ (a cos(θ) , a sin(θ))

Now, radius

$r=\sqrt{{g}^{2}+{f}^{2}-c}$

$\implies\,r=\sqrt{{a}^{2}\cos^{2}(\theta)+{a}^{2}\sin^{2}(\theta)-0}$

$\implies\,r=\sqrt{{a}^{2}\left(\cos^{2}(\theta)+\sin^{2}(\theta)\right)}$

$\implies\,r=a$