Radius of the circle x 2 + y 2 – 4x + 2y – 31 = 0 is
| Radius of the circle x2 + y2 – 4x + 2y – 31 = 0 is
A. 4 units
B. 2 units
C. 6 units
D. 31 units
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
The general second degree equation of a circle in x and y is given by: a ⋅ x2 + a ⋅ y2 + 2gx + 2fy + c = 0 with centre (-g, -f) and radius
\(r = \sqrt{{g^2} + {f^2} - c} \).
Calculation:
Given: x2 + y2 - 4x +2y - 31 = 0 are equation of circle with centres C1 and radius r1
By comparing the equation of the circle with the equation ax2 + ay2 + 2gx + 2fy + c = 0, we get a = 1, g = - 2, f = 1 and c = -31.
\(r = \sqrt{{g^2} + {f^2} - c} \)
\(r = \sqrt{{4} + {1} - (-31)} \)
r = 6 unit