Equation of a Circle: Geometry Math Test – PDF Download

Question 1: Write the equation (2 points)

Write the equation of the circle with center \((-4,3)\) and radius 6.

Question 2: Equation from a graph (2 points)

Write the equation of the circle shown. The center is at a lattice point, and the circle passes through (5, −1).

Question 3: Center and radius (2 points)

Find the center and the exact radius of the circle \((x+3)^{2}+(y-7)^{2}=50\).

Question 4: Points and a circle (3 points)

The circle \((x-1)^{2}+(y-2)^{2}=25\) is shown. Decide whether each point is inside, on, or outside the circle. Show the calculation. A\((4,6)\), B\((-2,3)\), C\((6,5)\).

Question 5: Complete the square (3 points)

The equation of a circle is \(x^{2}+y^{2}-4x+10y+13=0\). Rewrite it in standard form, and state the center and the radius.

Question 6: Diameter endpoints (2 points)

A circle has a diameter with endpoints \((-3,-2)\) and \((5,4)\). Write the equation of the circle.

Question 7: Tangent circle (2 points)

A circle has center \((6,-4)\) and is tangent to the x-axis. Write its equation.

Question 8: Derive the equation (2 points)

The circle shown has center \((h,k)\) and radius \(r\). Use the right triangle to show that every point \((x,y)\) on the circle satisfies the circle equation.

Question 9: Points on a circle (2 points)

The point \((5,y)\) lies on the circle \(x^{2}+y^{2}=169\). Find all possible values of \(y\).

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