A circle with a radius of 10 and a center (0,2) is given. It is required to find the equation in standard form for the circle.
Recall that the Standard Form of the Equation of a Circle with center (h,k), and radius, r is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Substitute the center (h,k)=(0,2) and the radius, r=10 into the formula:
[tex](x-0)^2+(y-2)^2=10^2[/tex]
Simplify the expressions:
[tex]\Rightarrow x^2+(y-2)^2=100[/tex]
Hence, the required equation in standard form is x²+(y-2)²=100.
