Question

The radius of the circle with centre at \((-4, 0)\) and passing through the point \((2, 8)\) is:

• A. 6
• B. 8
• C. 10
• D. 12
• E. 14

Hint:

Always check that the coordinates substituted into the distance formula are correct to ensure accuracy in calculating distances, particularly for circle geometry problems.

Answer 1

The Correct Option is C

The radius \( r \) of a circle is the distance from the center of the circle to any point on the circle. 
Given the center of the circle \((-4, 0)\) and a point on the circle \((2, 8)\), we use the distance formula to find \( r \): \[ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates of the center and the point: \[ r = \sqrt{(2 - (-4))^2 + (8 - 0)^2} \] \[ = \sqrt{(2 + 4)^2 + 8^2} \] \[ = \sqrt{6^2 + 8^2} \] \[ = \sqrt{36 + 64} \] \[ = \sqrt{100} \] \[ = 10 \] Thus, the radius of the circle is \( 10 \).