A circle has its centre at \(C(1,\,-3)\) and passes through the point \(A(-8,\,9)\). What is the circumference of the circle?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(30\pi\) units
The radius is the distance from the centre to any point on the circle, found with the distance formula; the circumference is \(2\pi r\).
Horizontal gap: \(-8-1=-9\), and \((-9)^2=81\)
Vertical gap: \(9-(-3)=12\), and \(12^2=144\)
\(r^2=81+144=225\), so \(r=15\)
Circumference \(=2\pi r=2\pi\times15=30\pi\) units
