Eliminate the parameter then write the resulting equation m

Eliminate the parameter, then write the resulting equation m standard form for the given situation. A circle: x = h + r cos t, y = k + r sin t Write the resulting equation in standard form.

Solution

given x=h+rcost   ==>cost=(x-h)/r

    y=k+rsint   ==> sint=(y-k)/r

We know by trigonometric identity

cos^2(t)+ sin^2(t)=1

==> (x-h)^2/r^2 + (y-k)^2 /r^2 =1 ........Ans