Question
Question: The pair of straight line joining the origin to the points of intersection of the line y = \(2\sqrt{...
The pair of straight line joining the origin to the points of intersection of the line y = 22x + c and the circle
x2 + y2 = 2 are at right angles, if-
A
c2 – 9 = 0
B
c2 – 10 = 0
C
c2 – 4 = 0
D
c2 – 8 = c
Answer
c2 – 9 = 0
Explanation
Solution
By homogenizing the equation of lines joining
origin and points of intersection of line
y = 22x + c with the circle x2 + y2 = 2 is
x2 + y2 = 2 (cy−22x)2
for perpendicular lines coefficient of x2 + coefficient of y2 = 0
1 – c216+ 1 – c22= 0
c2 – 9 = 0
c2 = 9