Question
Question: The points (4, –2) & (3, b) are conjugate w.r.t. the circle x<sup>2</sup> + y<sup>2</sup> –2x + 4y ...
The points (4, –2) & (3, b) are conjugate w.r.t. the circle
x2 + y2 –2x + 4y + 1 = 0 for
A
bÎ R
B
No value of b
C
b Î Q
D
None
Answer
No value of b
Explanation
Solution
Polar of (4, –2) w.r.t. the circle
x2 + y2 –2x + 4y + 1 = 0
is 4x – 2y – (x +4) + 2 (y –2) + 1 = 0 (T = 0)
i.e. 3x – 7 = 0
(3, b) is conjugate to (4, –2) if it lies on the polar of (4, –2) but (3, b) does not lie on the polar 3x – 7 = 0 for any value of b so, (4, –2) and (3, b) are not conjugate for any b