Question
Question: The equation of a circle through the intersection of x<sup>2</sup> + y<sup>2</sup> + 2x = 0 and x– y...
The equation of a circle through the intersection of x2 + y2 + 2x = 0 and x– y= 0 having minimum radius is-
A
x2 + y2 = 1
B
x2 + y2 –x – y = 1
C
x2 + y2 + x + y =0
D
None of these
Answer
x2 + y2 + x + y =0
Explanation
Solution
Intersection point of circle and line become end points of diameter of circle [Minimum radius]
x2 + y2 + 2x = 0; x – y = 0
Ю x2 + x2 + 2x = 0 Q x = y
Ю 2x2 + 2x = 0; Ю x (x +1) = 0
Ю x = 0, y = 0 & x = –1, y = –1
Eqn of circle (x – 0)(x + 1) + (y – 0)(y +1) = 0
Ю x2 + x + y2 + y = 0 Ю x2 + y2 + x + y = 0