Circle IIT JEE questions from Kota coachings (Type 1)
Section (A) Equation of circle, parametric equation, position of a point
A-1. The radius of the circle passing through the points (1, 2), (5, 2) & (5, 2) is:
[15JM110320]
(A) 52
(B) 21/5
(c) 3/2
(D) 2 2
A-1. The radius of the circle passing through the points (1, 2), (5, 2) & (5, 2) is:
[15JM110320]
(A) 52
(B) 21/5
(c) 3/2
(D) 2 2
A-2. The centres of the circles x2 + y2-6x-8y-7 = 0 and x2 + y2
-4x-10y-3 = 0 are the ends of the
[16JM110499]
also find
16JM1104
diameter of the circle
(A) x2 + y2-5x-9y + 26 = 0
(C) x2 y + 5x -y 14 0
(B) x2 + y 5x - 9y 14 0
(D) x2 t ya 5x y14 0
nget
A-3. The circle described on the line joining the points (0. 1), (a. b) as diameter cuts the x axis in points
(15JM110321]
meter cuts the x-axis in points
whose abscissa are roots of the equation:
(A) x2 + ax + b=0 (B) x2-ax + b=0
(C) x2 +ax-b=0
(D) x2-ax-b=0
A-4. The intercepts made by the circle x2 + y?- 5x 13y 14 O on the x axis and y-axis are respectively
(D) none [16JM110500]
(A) 9, 13
(B) 5, 13
(C) 9, 15
(D) NoneM110315
A-5. Equation of line passing through mid point of intercepts made by circle x2 y-4x-6y 0 on
M110316
[15JM110322]
co-ordinate axes is
(B) 3x + y-6-0
(C) 3x + 4y-12-0
(D) 3x + 2y-6-0
(A) 3x + 2y-12-0
the circk
M110
A-6. Two thin rods AB & CD of lengths 2a & 2b move along Ox &
OY respectively, when 'O is the origin The
equation of the locus of the centre of the circle passing through the extremities of the two rods
[15JM110347]
(A)-x²+y²=a²+b²
(B)x²-y2=a²-b2
(C)x²+y²=a²-b²
(D)x²-y²=a²+b²
A-7.
Let A and B be two fixed points then the locus of a point C which moves so that (tant BAC)(tan,ABC)=1,0<BAC<π/2,0<ABC<π/2 is
(A)Circle
(B)pair of straight line
(C)A point
(D) Straight line
A-8.STATEMENT-1
: The length of intercept made by the circle x2+y2-2x-2y=0
on the x-axis is 2.
STATEMENT-2 : x2 + y2-ax-By = o is a circle which passes through ongin with centre (a/2,B/2) and
radius √a2+b²/2.
(A) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is correct explanation for
(B) STATEMENT-1 is true, STATEMENT-2 is true and STATEMENT-2 is not correct explanation for
(C)STATEMENT-1 is true, STATEMENT-2 is false
(D)STATEMENT-1 is false, STATEMENT-2 is true
Section (B) : Line and circle, tangent, pair of tangents
B-1.Find the co-ordinates of a point p on line x + y =-13, nearest to the circle x2 + y2 + 4x + 6y-s-o
(A)(-6,-7)
(B)(-15,2)
(C)-5,-6)
(D) (-7,-6) (15JM110324]
B-2. The number of tangents that can be drawn from the point (8, 6) to the circle x²+ y²+4x+6y-5
=0 is
(A) 0
(B) 1
(C) 2
(D) none [15JM110325]
B-3. Two lines through (2, 3) from which the circle x2+y²=25 intercepts chords of length 8 units have
equations
(A) 2x + 3y = 13, x + 5y = 17
(C) x-2, 9x-11y=51
(B) y = 3, 12x+5y = 39
(D) y = 0, 12x+5y = 39
Circle
Circle
Ci
[16JM110501s
B-4.
B-4.The line 3x + 5y + 9-0 w.rt, the circle x2 + y2-4x + 6y + 5 = 0 is
(A) chord dividing circumference in 1:3 ratio
(C) tangent
(B) diameter
(D) outside line
B-5.
If one of the diameters of the circle x2 + y2-2x-6y + 6 = o is a chord to the circle with centre (2, 1),
then the radius of the circle is
(15JM 110333]C
(A) 3
(B) 2
(C) 3/2
(D) 1
B-6.The tangent lines to the circle x2 + y2-6x + 4y-12 which are parallel to the line 4x + 3y + 5
given by
(A) 4x + 3y-7=0, 4x + 3y + 15=0
0 are
[16JM110502]
(B) 4x + 3y-31 = 0, 4x+3y + 19 = 0
(D) 4x + 3y-31=0, 4x + 3y-19=0
(C) 4x +3y 17 0, 4x +3y 130
B-7.The condition so that the line (x + g) cosθ + (y + f) sin θ = k is a tangent to x2 + y2 + 2gx + 2fy +c
[15JM110327)
(A) g2 + R = c + k2
(B) g2 + f2 = c2 + k
(C) g2 + f2 = C2 + k2
(D) g2 + f2 = c + k
B-8. The tangent to the circle x2+ y 5 at the point (1,-2) also touches the circle (15JM110328]
x2 + y2-8x+6y + 20 = 0
(A)(-2,1)
(B)(-3,0)
(C)(-1,-1)
(D)(-3,1)
B-9.The angle between the two tangents from the origin to the circle (x-774 (y+1 )2-25 equals
A.π\4
B.π\3
C.π\2
D.π\6
B-10.
A point A(2, 1) is outside the circle x2+y2+2gx+2fy + c = 0 & AP AQ are tangents to the circle. The
equation of the circle circumscribing the triangle APQ is[16JM110503
(A) (x +g) (x-2)+ (y+f) (y-1)0
(B) (x + g) (x-2)-(y+D(y-1)=0
C.(x-g)(X+2)+(y-f)(y+1)=0
D.(x-g)(x-2)+(y-f)(y-1)=0
B-11.A line segment through a point P cuts a given circle in 2 points A & B, such that PA= 16 & PB-9, find
the length of tangent from points to the circle
(A) 7
(B) 25
(C) 12
(D) 8
B-12. The length of the tangent drawn from any point on the circle x²+y² + 2gx+2fy+p= 0 to the circle
[16JM110504
(A) √q-p
(B)√ p-q
(C) √p+q
(D)√2q+p
B-13. The equation of the diameter of the circle (x - 2)2 +(y+1)2 =16 which bisects the chord cut off by the
circle on the line x-2y-3=0is
(A) x + 2y = 0
(B) 2x ty -3 0 (C) 3x + 2y-4 0 (D) 3x -2y-4 0
B-14. The locus of the point of intersection of the tangents to the circle x2 + y
a2 at points whose parametric
angles differ by
π/3 is
[16JM110505
(A) x²+y²=4a²/3
(B) x2 + y2 =2a²/3
(C) x2 + y2 =a²/3
(D) x2 + y2 =a²/9
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