The equation of a circle with centre $$$C$$$ is $$$x^{2}+y^{2}-8 x+4 y-5=0$$$. Find the radius of the circle and the coordinates of $$$C$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_12 Year：2020 Question No：11(a)

Answer:

Express as $(x-4)^{2}+(y+2)^{2}=16+4+5$
Centre $C(4,-2)$
Radius $=\sqrt{25}=5$

1.1.1 carry out the process of completing the square for a quadratic polynomial and use a completed square form

1.3.3 understand that the equation represents the circle with centre and radius (Including use of the expanded form.)