CircleHard
Question
Equations of circles which pass through the points (1, _2) and (3, _ 4) and touch the x-axis is
Options
A. x2 +
y2 + 6x + 2y + 9 = 0
B.
x2 + y2 + 10x + 20y + 25 = 0
C. x2 +
y2 _ 6x + 4y + 9 = 0
D. none
Solution
Let equation of required circle is
x2 + y2 + 2gx + 2fy + c = 0
it passes through (1, _2) & (3, _4)
2g _ 4f + c = _5
6g _ 8f + c = _25
4g _ 8f + 2c = _10
6g _ 8f + c = _25
_2g + c = 15
circle touches x-axis g2 = c Þ
g2 _ 2g _ 15 = 0
g = 5, _ 3
g = 5, c = 25, f = 10 Þ x2 + y2 + 10x + 20y + 25 = 0
g = _3, c = 9, f= 2 Þ x2 + y2 _ 6x + 4y + 9 = 0
