SATMathematics Practice Test 1

The equation of a circle can be written as ${\left(\mathit{x}-\mathit{h}\right)}^2+{\left(\mathit{y}-\mathit{k}\right)}^2={\mathit{r}}^2$ where$\left(\mathit{h},\mathit{k}\right)$ are the coordinates of the center of the circle and r is the radius of the circle.
Since the coordinates of the center of the circle are (0, 4), the equation is ${\mathit{x}}^2+{\left(\mathit{y}-4\right)}^2)={\mathit{r}}^2$ The radius of the circle is the distance from the center, $\left(0,4\right),$ to the given endpoint of a radius $\left(\frac{4}{3},5\right)$.
By the distance formula .
Therefore, an equation of the given circle is ${\mathit{x}}^2+{\left(\mathit{y}-4\right)}^2=\frac{25}{9}$
Choice B is incorrect; it results from the incorrect equation ${\left(\mathit{x}+\mathit{h}\right)}^2+{\left(\mathit{y}+\mathit{k}\right)}^2={\mathit{r}}^2$.
Choice C is incorrect; it results from using r instead of ${\mathit{r}}^2$ in the equation for the circle.
Choice D is incorrect; it results from using the incorrect equation ${\left(\mathit{x}+\mathit{h}\right)}^2+{\left(\mathit{y}+\mathit{k}\right)}^2=\frac{1}{\mathit{r}}$