Calculating the equation of a circle

Practice Questions

GMAT Quantitative Reasoning › Calculating the equation of a circle

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In the -plane, point $(a,b)$ lies on a circle with center at the origin. The radius of the circle is 5. What is the value of $a^{2}+b^{2}$ ?

The points and form a line which passes through the center of circle Q. Both points are on circle Q.

Which of the following represent the correct equation for circle Q?

Two circles on the coordinate plane have the origin as their center. The inner circle has as its equation

$x^{2}+ y^2 = 64$ ;

the region between the circles has area $30 \pi$ .

Give the equation of the outer circle.

$\textup{Circle }Q$ is centered at the point $\left ( -6,-5\right )$ and touches the y-axis once at the point $\left ( 0,-5\right )$ . What is the equation for $\textup{Circle }Q$ ?

Two circles on the coordinate plane have the origin as their center. The outer circle has twice the circumference as the inner circle, the equation of which is

$x^{2}+ y^{2} = 16$ .

Give the equation of the outer circle.

Two circles on the coordinate plane have the origin as their center. The outer circle has as its equation

$x^{2}+ y^2 = 50$ ;

the inner circle has as its equation

$x^{2}+ y^2 = 25$ .

Give the area of the region between the two circles.

Two circles on the coordinate plane have the origin as their center. The outer circle has as its equation

$x^{2}+ y^2 = 64$ ;

the region between the circles has area $30 \pi$ .

Give the equation of the inner circle.

Two circles on the coordinate plane have the origin as their center. The outer circle has twice the area as the inner circle, the equation of which is

$x^{2}+ y^{2} = 5$ .

Give the equation of the outer circle.

Two circles on the coordinate plane have the origin as their center. The outer circle has area five times that of the inner circle; the region between them has area $20 \pi$ . Give the equation of the inner circle.

Find the equation of circle whose radius is and center is at .

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