Relative position of two circles: meeting points and common tangents
This type of question, asked 7 times: 2021 Paper 7, 2021 Paper 9, 15 Apr 2023, 30 Jan 2024, 1 Feb 2024, 22 Jan 2025, 22 Jan 2026 S1. All 7 questions below, oldest first.
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Question 1
2021 Paper 7
77
Choose the incorrect statement about the two circles whose equations are x2+y2−10x−10y+41=0 and x2+y2−16x−10y+80=0:
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Question 2
2021 Paper 9
65
Choose the correct statement about two circles whose equations are given below:
x2+y2−10x−10y+41=0
x2+y2−22x−10y+137=0
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Question 3
15 Apr 2023
72
The number of common tangents, to the circles x2+y2−18x−15y+131=0 and x2+y2−6x−6y−7=0, is :
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Question 4
30 Jan 2024
74
If the circles (x+1)2+(y+2)2=r2 and x2+y2−4x−4y+4=0 intersect at exactly two distinct points, then
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Question 5
1 Feb 2024
78
Let C:x2+y2=4 and C′:x2+y2−4λx+9=0 be two circles. If the set of all values of λ so that the circles C and C′ intersect at two distinct points, is R−[a,b], then the point (8a+12,16b−20) lies on the curve:
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Question 6
22 Jan 2025
64
A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2,5) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval (α,β), then 3β−2α is equal to :
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Question 7
22 Jan 2026 S1
62
Let the set of all values of r , for which the circles (x+1)2+(y+4)2=r2 and x2+y2−4x−2y−4=0 intersect at two distinct points be the interval ( α, β ). Then αβ is equal to
