Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let the circle S : 36x 2 + 36y 2 − 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 :
A
B
100 < C < 165
C
81 < C < 156
D
100 < C < 156
Text Solution
Verified by ExpertsThe correct answer is:
D
S : 36x 2 + 36y 2 − 108x + 120y + C = 0
Centre 
radius 
Now, 
⇒ C > 100 …. . (1)
Now point of intersection of x − 2y = 4 and 2x − y = 5 is (2,−1), which lies inside the circle S.
∴ S(2,−1) < 0
From (1) & (2)
100<C<156
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
In the circle given below, let unit, unit and . Then, the area of the triangle
(in square units…
Let and be two points. Let be a point on the circle such that
have maximum value, then the poi…
Let the lengths of intercepts on -axis and -axis made by the circle be and , respectively. The…
The line is a tangent to the circle at the point and the centre of the circle lies on . Then, th…
Choose the incorrect statement about the two circles whose equations are given below:
and
Two tangents are drawn from a point to the circle , such that the angle betweenthese tangents is …