JEE Main Previous Year Questions (2025): Circle

 Page 1


JEE Main Previous Year Questions 
(2025): Circle 
Q1. The absolute difference between the squares of the radii of the two circles passing 
through the point (-?? , ?? ) and touching the lines ?? + ?? = ?? and ?? - ?? = ?? , is equal to 
____ . 
Ans: 768 
Solution:  
 
Centre ( a, 0 ) 
r = |
a - 0 - 3
v2
|
 circle (?? - ?? )
2
+ ?? 2
= (
?? - 3
v2
)
2
 
passes through (-9,4) 
2(?? 2
+ 18?? + 81 + 16) = (?? 2
- 6?? + 9)
a
2
+ 42a + 185 = 0
 (?? + 37)(?? + 5) = 0
 ? ?? = -37, -5
?? 1
= |
-37 - 3
v2
| = 20v2
r
2
= |
-5 - 3
v2
| = 4v2
|?? 1
2
- ?? 2
2
| = |800 - 32| = 768
 
 
Page 2


JEE Main Previous Year Questions 
(2025): Circle 
Q1. The absolute difference between the squares of the radii of the two circles passing 
through the point (-?? , ?? ) and touching the lines ?? + ?? = ?? and ?? - ?? = ?? , is equal to 
____ . 
Ans: 768 
Solution:  
 
Centre ( a, 0 ) 
r = |
a - 0 - 3
v2
|
 circle (?? - ?? )
2
+ ?? 2
= (
?? - 3
v2
)
2
 
passes through (-9,4) 
2(?? 2
+ 18?? + 81 + 16) = (?? 2
- 6?? + 9)
a
2
+ 42a + 185 = 0
 (?? + 37)(?? + 5) = 0
 ? ?? = -37, -5
?? 1
= |
-37 - 3
v2
| = 20v2
r
2
= |
-5 - 3
v2
| = 4v2
|?? 1
2
- ?? 2
2
| = |800 - 32| = 768
 
 
Q2. If the four distinct points (?? , ?? ), (-?? , ?? ), (?? , ?? ) and (?? , ???? ) lie on a circle of radius 
r , then ?????? + ?? ?? is equal to 
A. 32 
B. 33 
C. 34 
D. 35 
Ans: D 
Solution: 
 
m
1
 m
2
= -1 so right angle equation circle is 
 (?? - 4)(?? - 0) + (?? - 6)(?? - 0) = 0
?? 2
+ ?? 2
- 4?? - 6?? = 0
 (?? , 3?? ) lies on it so 
?? 2
+ 9?? 2
- 4?? - 18?? = 0
10?? 2
- 22?? = 0
?? = 0,
11
5
 
?? = 0 is not possible so ?? =
11
5
 
 also ?? = v4 + 9 = v13
 so 10?? + ?? 2
= 10 ·
11
5
+ (v13)
2
= 35
 
 
Q3. Let ?? ?? be the circle in the third quadrant of radius 3 , that touches both coordinate 
axes. Let ?? ?? be the circle with centre (?? , ?? ) that touches ?? ?? externally at the point 
(?? , ?? ). If (?? - ?? )
?? =
?? ?? , ?????? (?? , ?? ) = ?? , then ?? + ?? is equal to : 
A. 9 
B. 13 
Page 3


JEE Main Previous Year Questions 
(2025): Circle 
Q1. The absolute difference between the squares of the radii of the two circles passing 
through the point (-?? , ?? ) and touching the lines ?? + ?? = ?? and ?? - ?? = ?? , is equal to 
____ . 
Ans: 768 
Solution:  
 
Centre ( a, 0 ) 
r = |
a - 0 - 3
v2
|
 circle (?? - ?? )
2
+ ?? 2
= (
?? - 3
v2
)
2
 
passes through (-9,4) 
2(?? 2
+ 18?? + 81 + 16) = (?? 2
- 6?? + 9)
a
2
+ 42a + 185 = 0
 (?? + 37)(?? + 5) = 0
 ? ?? = -37, -5
?? 1
= |
-37 - 3
v2
| = 20v2
r
2
= |
-5 - 3
v2
| = 4v2
|?? 1
2
- ?? 2
2
| = |800 - 32| = 768
 
 
Q2. If the four distinct points (?? , ?? ), (-?? , ?? ), (?? , ?? ) and (?? , ???? ) lie on a circle of radius 
r , then ?????? + ?? ?? is equal to 
A. 32 
B. 33 
C. 34 
D. 35 
Ans: D 
Solution: 
 
m
1
 m
2
= -1 so right angle equation circle is 
 (?? - 4)(?? - 0) + (?? - 6)(?? - 0) = 0
?? 2
+ ?? 2
- 4?? - 6?? = 0
 (?? , 3?? ) lies on it so 
?? 2
+ 9?? 2
- 4?? - 18?? = 0
10?? 2
- 22?? = 0
?? = 0,
11
5
 
?? = 0 is not possible so ?? =
11
5
 
 also ?? = v4 + 9 = v13
 so 10?? + ?? 2
= 10 ·
11
5
+ (v13)
2
= 35
 
 
Q3. Let ?? ?? be the circle in the third quadrant of radius 3 , that touches both coordinate 
axes. Let ?? ?? be the circle with centre (?? , ?? ) that touches ?? ?? externally at the point 
(?? , ?? ). If (?? - ?? )
?? =
?? ?? , ?????? (?? , ?? ) = ?? , then ?? + ?? is equal to : 
A. 9 
B. 13 
C. 22 
D. 31 
Ans: C 
Solution: 
 
Let C
1
 and C
2
 has centres ?? (-3
1
- 3) and ?? (1,3) 
AB = v16 + 36 = 2v13
r
1
= 3 and r
2
= 2v13 - 3
P(?? , ?? ), ?? =
r
1
(1) + r
2
(-3)
r
1
+ r
2
, ?? =
r
1
(3) + r
2
(-3)
r
1
+ r
2
?? =
3 - 3(2v13 - 3)
2v13
, ?? =
18 - 6v13
2v13
 (?? - ?? )
2
= (
6
2v13
)
2
 (?? - ?? )
2
= (
6
2v13
)
2
, m + n = 22