WT-7(CIRCLE)
Single Correct Type: (+3, –1) Time: 60 Mints.
1. If the circumference of the circle x y 8 x 8 y b 0 is bisected by x y 2 x 4 y a 0 , then a + b is
2 2 2 2
equal to
(A) – 56 (B) 2 (C) – 64 (D) – 14
2. Given a circle ( x 4)2 ( y 2) 2 25 . Another circle is drawn passing through (–4, 2) and touching the given
circle internally at the point A (–4, 7). AB is the chord of length 8 units of the larger circle intersecting the other
circle at the point C. The AC will be
(A) 4 units (B) 17 units (C) 5 units (D) 3 units
3. The sum of the squares of the lengths of the chords intercepted on the circle, x 2 y 2 16 , by the lines,
x y n, n N , where N is the set of all natural numbers, is
(A) 320 (B) 105 (C) 160 (D) 210
4. A circle is drawn through the point of intersection A and B of the curve 2x 2 3y 5x 8 0
and the line y 7x 0 , the length of tangent drawn from origin to the circle is equal to
(A) 2 (B) 2 2 (C) 4 2 (D) 4
5. Let S1 and S2 be two externally tangent circles having the same radius ‘r’. Let L be a direct common tangent to
S1 and S2. If Sn be circle such that it touches Sn – 1 and S1 externally and line L, n 3, n N then radius of S2022
is
r r r
(A) r (B) (B) (D)
2021 2021
2 3
2021
One or more Correct type: (+4, –1)
6. Consider the circles
S1 x 2 y 2 3x 2 y 1 0 S2 : x 2 y 2 x 6 y 5 0
S3 x 2 y 2 5 x 8 y 15 0
Also let S 4 be a circle which cuts S1 , S 2 , S3 orthogonally. Then identify the correct statements from the
following
(A) Point from which length of tangents to S1 , S 2 , S3 are equal is (3, 2) (B) Radius of S 4 is 3 3
3 8
(C) Radical centre of S1 , S2 , S4 is , (D) Centre of S 4 is (3, 2)
5 5
7. Suppose line x – 2y + 1 = 0, mx + y + 3 = 0 meet co-ordinate axes in concyclic point, then
5
(A) m = –2 (B) the circle cuts a chord of length on x – axis
2
(C) radius of circle is 2 (D) a parabola can not pass through above four points
8. A circle is drawn with centre (, ) : is rational and is irrational, then
(A) there exist at most two rational points on the circle
(B) if there exist exactly two rational points P and Q on the circle then slope of PQ must be 0
(C) if there exist only one point R(x1, y1) on circle with 2, 3 as centre then radius must be irrational
(D) for exactly one rational point R(x1, y1) on circle with 2, 3 as centre then x1 = 1
FIITJEE KOLKATA NORTH CENTRE,NEEPCO BUILDING, CIT Road, Beside Uttarapan Market, Kolkata – 48, Ph.– 03323556700, northkolkata@fiitjee.com, 1
M.AS
www.fiitjeekolkatanorth.com, FIITJEE National Office:29-A, Kalu Sarai , Sarvapriya Vihar, New Delhi, Delhi -110016, Ph: 011-46106000, www.fiitjee.com
CIRCLE
1 1
9. Given circles C1 : x 1 x 2 y 1 y 0, C2 : x 1 x 3 y 1 y 0 ,
2 3
1 1
C3 : x 2 x 3 y y 0 . Let their points of intersection form ABC, then which of the
2 3
following holds true?
11 11
(A) Centroid of ABC is 2, (B) Orthocentre of ABC is , 4
18 18
37 81 11
(C) Circumcentre of ABC is , (D) Centroid of C1C2C3 (centres) is 2,
12 16 18
Integer Type: (+3, –1)
10. The centre of variable circle x 2 y 2 2 gx 2 fy c 0 lies on the line 2 x – 2 y 9 0 and the variable circle
cuts the circle x 2 y 2 4 orthogonally if the variable circle passes through two fixed points (a, b) and (c, d)
where (b < d) then the value of 2b + d is
11. Two circles of unequal radii have four common tangents. A transverse common tangent meets the direct
common tangents at the points P & Q. If length of direct tangent (between the point of contacts) is 8 then length
of PQ is.
12. Let C1 x2 + y2 – 169 = 0 and C2 x2 + y2 – 24x – 32y + 111 = 0. Let AB be their common chord.
Maximum area of ABC if C lies on minor arc AB, is
13. If length of smallest path that can be traced from (0, 0) to
2 1, 1 without traversing inside the curve
a
x 2 y 2 2 2x 1 0 is of the form b ; a, b I , then value of a b is
16
--------
ANSWER KEY
1. A 2. A 3. D 4. D 5. C
6. ABCD 7. AB 8. ABC 9. ACD 10. 5
11. 8 12. 65.72 13. 2 14. 15.
FIITJEE KOLKATA NORTH CENTRE,NEEPCO BUILDING, CIT Road, Beside Uttarapan Market, Kolkata – 48, Ph.– 03323556700, northkolkata@fiitjee.com, 2
M.AS
www.fiitjeekolkatanorth.com, FIITJEE National Office:29-A, Kalu Sarai , Sarvapriya Vihar, New Delhi, Delhi -110016, Ph: 011-46106000, www.fiitjee.com
