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Mere Teacher · Previous Year Questions
JEE Main Mathematics · Circle · Set 2 (Q31-60)
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31.
If P and Q are the points of intersection of the circles x2+y2+3x+7y+2p−5=0 and x2+y2+2x+2y−p2=0, then there is a circle passing through P,Q and (1,1) for :
(1)all except one value of p
(2)all except two values of p
(3)exactly one value of p
(4)all values of p
32.
The centre of the circle passing through the point (0,1) and touching the parabola y=x2at thepoint (2,4) is:
(1)(10−53,516)
(2)(56,1053)
(3)(5−16,1053)
(4)(103,516)
33.
A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then
(1)radius of S is 8
(2)radius of S is 7
(3)centre of S is (–7, 1)
(4)centre of S is (–8, 1)
34.
The circle passing through the intersection of the circlesx2+y2−6x=0 and x2+y2−4y=0having its centre on the line, 2x−3y+12=0 also passes through the point:
(1)(−3,6)
(2)(−1,3)
(3)(−3,1)
(4)(1,−3)
35.
The intercept on the line y=x by the circle x2+y2−2x=0 is AB. The equation of the circle with AB as a diameter is
(1)x2+y2+x+y=0
(2)x2+y2−x−y=0
(3)x2+y2−3x+y=0
(4)x2+y2+3x−y=0
36.
Let y=x be the equation of a chord of the circle C1 (in the closed half-plane x≥0 ) of diameter 10 passing through the origin. Let C2 be another circle described on the given chord as its diameter. If the equation of the chord of the circle C2, which passes through the point (2,3) and is farthest from the center of C2, is x+ay+b=0, then a−b is equal to
(1)-2
(2)10
(3)-6
(4)6
37.
Let a circle passing through (2,0) have its centre at the point (h,k). Let (xc,yc) be the point of intersection of the lines 3x+5y=1 and (2+c)x+5c2y=1. If h=limc→1xc and k=limc→1yc, then the equation of the circle is :
(1)25x2+25y2−2x+2y−60=0
(2)5x2+5y2−4x+2y−12=0
(3)5x2+5y2−4x−2y−12=0
(4)25x2+25y2−20x+2y−60=0
38.
Let the tangents at the points A(4,−11) and B(8,−5) on the circle x2+y2−3x+10y−15=0, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to
(1)433
(2)213
(3)13
(4)3213
39.
If a variable line, 3x+4y−λ=0 is such that the circles x2+y2−2x+2y+1=0 and x2+y2−18x−2y+78=0 are on its opposite sides, then the set of all values λ is the interval:
(1)(2, 17)
(2)[13, 23]
(3)[12, 21]
(4)(23, 31)
40.
The circle passing through the point (–1, 0) and touching the y-axis at (0, 2) also passes through the point
(1)(2−3,0)
(2)(2−5,2)
(3)(2−3,25)
(4)(–4, 0)
41.
Let a variable line passing through the centre of the circle x2+y2−16x−4y=0, meet the positive coordinate axes at the point A and B. Then the minimum value of OA+OB, where O is the origin, is equal to
(1)12
(2)18
(3)20
(4)24
42.
Let S={z∈C:z−2iz−6i=1 and z+2iz−8+2i=53}. Then ∑z∈S∣z∣2 is equal to
(1)385
(2)398
(3)413
(4)423
43.
Find the equation of a circle of radius 5 units whose centre lies on x-axis and passes through the point (2,4).
(1)x2+y2−12x−11=0
(2)x2+y2−4x−21=0
(3)x2+y2+2x−24=0
(4)x2+y2+12x−11=0
44.
Let the tangents drawn from the origin to the circle, x2+y2−8x−4y+16=0touch it at the point A and B. The (AB)2 is equal to:
(1)564
(2)524
(3)58
(4)138
45.
If the circles (x+1)2+(y+2)2=r2 and x2+y2−4x−4y+4=0 intersect at exactly two distinct points, then
(1)5<r<9
(2)0<r<7
(3)3<r<7
(4)21<r<7
46.
The parametric equation of the circle x2+y2−6x−2y+9=0 are
(1)x=3+cosθ,y=1+sinθ
(2)x=1+cosθ,y=3+sinθ
(3)x=cosθ,y=sinθ
(4)x=3+sinθ,y=1+cosθ
47.
If a line, y=mx+c is a tangent to the circle, (x−3)2+y2=1and it is perpendicular to a line L1 where L1 is the tangent to the circle, x2+y2=1 at the point (21,21)
(1)c2+6c+7=0
(2)c2−6c+7=0
(3)c2+6c−7=0
(4)c2−6c−7=0
48.
The set of values of k for which the circle C : 4x2+4y2-12x + 8y+k=0 lies inside the fourth quadrant and the point (1,−31) lies on or inside the circle C is :
(1)An empty set
(2)(6,995]
(3)[980,10)
(4)(9,992]
49.
The centre of the circle whose radius is 3 units and touching internally the circle x2+y2−4x−6y−12= 0 at the point (−1,−1) is
(1)(54,57)
(2)(54,5−7)
(3)(5−4,5−7)
(4)(5−4,57)
50.
Let a circle C1 be obtained on rolling the circle x2+y2−4x−6y+11=0 upwards 4 units on the tangent T to it at the point (3,2). Let C2 be the image circles C1 and C2 respectively, and M and N be respectively the feet of perpendiculars drawn from A and B on the x-axis. then the area of the trapezium AMNB is
(1)2(2+2)
(2)4(1+2)
(3)3+22
(4)2(1+2)
51.
If the line 3x+4y−1=0 touches the circle (x−1)2+(y−2)2=r2, then the value of r will be
52.
A circle with centre (2,3) and radius 4 intersects the line x+y=3 at the point P and Q. If the tangents at P and Q intersect at the point S(α,β), then 4α−7β is equal to ________
53.
If the tangent at the point P on the circle x2+y2+6x+6y=2 meets the straight line 5x−2y+6=0 at a point Q on the y−axis, then the length of PQ is
54.
The point P(10,7) lies outside the circle x2+y2−4x−2y−20=0. The greatest distance of P from the circle is
55.
If the circles x2+y2+2x+2ky+6=0 and x2+y2+2ky+k=0 intersect orthogonally, then integral value of k is
56.
If the length of the tangents drawn from the point (1,2) to the circles x2+y2+x+y−4=0 and 3x2+3y2−x−y+k−0 be in the ratio 4:3, then k=−A/4. Find A.
57.
The equation of the image of the circle x2+y2+16x−24y+183=0 by the line mirror 4x+7y+13=0 is x2+y2+32x+4y+K=0. Find K.
58.
The straight line (x−2)+(y+3)=0 cuts the circle (x−2)2+(y−3)2=11 at how many points?
59.
The centers of a set of circles, each of radius 3 , lie on the circle x2+y2=25. The locus of any point in the set is 4≤x2+y2≤K. Find K.
60.
Let a circle C : (x−h)2 + (y−k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to_____.
