Question

Let the circle S : 36x² + 36y² – 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x – 2y = 4 and 2x – y = 5 lies inside the circle S, then :

(1) 25/9 < C < 13/3

(2) 100 < C < 165

(3) 81 < C < 156

(4) 100 < C < 156

Answer 1

Answer is: (4) 100 < C < 156

S : 36x²+36y² - 108x+120y+C = 0

Now point of intersection of x – 2y = 4 and 2x – y = 5 is (2, –1), which lies inside the circle S.