Question

For the two circles x kuadrat+y kuadrat=16 and x kuadrat+y kuadrat-2y=0,which the statement true?..a) there are two pairs of commons tangents. b) there are no common tangents. c)there are three common tangents. d)there is one pair of common tangents

Answer 1

X^2 + y^2 = 16 .... (1)
x^2 + y^2 - 2y = 0 .... (2)

subtract both equations, get
2y = 16
y = 8

subtitute y = 8 into one of equation above :
x^2 + y^2 = 16
x^2 + 8^2 = 16
x^2 + 64 = 16
x^2 = 16 - 64
x^2 = - 48
x = +- square root (- 64)

the value of x is unreal, which cause the two circles are no commont tangents (B)