Question

Determine standard from of the equation for the circle with center (h,k)=(-1/50,1/3),r=1/2

Answer 1

`\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-(1)/(50)}{ h},\stackrel{(1)/(3)}{ k})\qquad \qquad radius=\stackrel{(1)/(2)}{ r} \\\\\\ \left[ x-\left( -(1)/(50) \right) \right]^2+\left[ y-(1)/(3) \right]^2=\left( (1)/(2) \right)^2\implies \left( x+(1)/(50) \right)^2+\left( y-(1)/(3) \right)^2=(1^2)/(2^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( x+(1)/(50) \right)^2+\left( y-(1)/(3) \right)^2=(1)/(4)~\hfill`