JEE Questions for Maths Circle And System Of Circles Quiz 4

The values of λ, so that the line 3x - 4y = λ touches x² + y² - 4x - 8y - 5 = 0 are

0%
-35, 15
0%
3, -5
0%
35, -15
0%
-3, 5
0%
20, 15

A circle with centre at (2,is such that the line x + y + 2 = 0 cuts a chord of length 6. The radius of the circle is

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√41 cm
0%
√11 cm
0%
√21 cm
0%
√31 cm

The length of the common chord of the two circles x² + y² - 4y = 0 and x² + y² - 8x -4y + 11 = 0 is

0%
(√145/cm
0%
√11/2 cm
0%
√135 cm
0%
(√135/ 4 ) cm

The locus of the mid-points of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle x² + y² = 9 is

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20(x2 + y- 36x + 45y = 0
0%
20(x2 + y+ 36x - 45y = 0
0%
36(x2 + y- 20x - 45y = 0
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36(x2 + y+ 20x - 45y = 0

The radius of the circle, which is touched by the line y = x and has its centre on the positive direction of X-axis and also cuts-off a chord of length 2 units along the line √3y - x = 0 is

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√5
0%
√3
0%
√2
0%
1

The locus of the mid - points of the chords of the circle x² + y² = 4 which subtend a right angle at the origin is

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x2 + y2 = 1
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x2 + y2 = 2
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x + y = 1
0%
x + y = 2

The length of the chord joining points (4 cos θ, 4 sin θ) and [ 4 cos (θ + 60²), 4 sin (θ + 60^o)] of the circle x² + y² = 16 is

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4
0%
8
0%
16
0%
2

If two chords having lengths a² - 1 and 3(a + 1), where a is a constant of a circle bisect each other, then the radius of the circle is

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6
0%
15/2
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8
0%
19/2
0%
10

A line is drawn through the point P(3,to cut the circle x² + y² = 9 at A and B. Then PA . PB is equal to

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9
0%
121
0%
205
0%
139

The inverse of the point (1,with respect to the circle x² + y² - 4x - 6y + 9 = 0, is

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(1, 1/2)
0%
(2, 1)
0%
(0, 1)
0%
(1, o)

The length of the common chord of the circles x² + y² + 2x + 3y + 1 = 0 and x² + y² + 4x + 3y = 2= 0 is

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9/2
0%
2√2
0%
3√2
0%
3/2

The locus of the mid - point of the chord of the circle x² + y² - 2x - 2y - 2 = 0 which makes an angle of 120^o at the centre, is

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x2 + y2 - 2x - 2y - 1 = 0
0%
x2 + y2 + x + y - 1 = 0
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x2 + y2 - 2x - 2y + 1 = 0
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None of these

If C is the circle with centre (0,and radius 3 units. Then, the equation of the locus of the mid-points of the chords of the circle C that subtend an angle of 2π/3 at its centre, is

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x2 + y2 = 1
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x2 + y2 = 27/4
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x2 + y2 = 9/4
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x2 + y2 = 3/2

The equation of the circle whose diameter is the common chord of the circles x² + y² + 2x + 3y + 2 = 0 and x² + y² + 2x - 3y - 4 = 0 is

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x2 + y2 + 2x + 2y + 2 = 0
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x2 + y2 + 2x + 2y - 1 = 0
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x2 + y2 + 2x + 2y + 1 = 0
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x2 + y2 + 2x + 2y + 3 = 0

Let C be the circle with centre at (1,and radius 1. If T is the circle centred at (0, k) passing through origin and touching the circle C externally, then the radius of T is equal to

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√3/√2
0%
√3/2
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1/2
0%
1/4

The shortest distance between the circles (x - 1)² + (y + 2)² = 1 and (x + 2)² + (y - 2)² = 4 is

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1
0%
2
0%
3
0%
4
0%
5

If the circles x² + y² + 2gx + 2ty + c = 0 cuts the three circles x² + y² - 5 = 0, x² + y² - 8x - 6y + 10 = 0 and x² + y² - 4x + 2y - 2 = 0 at the extremities of their diameters, then

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c = - 5
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fg = 147/25
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g + 2f = c + 2
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4f = 3g

If the circles x² + y² + 2x + 2ky + 6 = 0 and x² + y² + 2ky + k = 0 intersect orthogonally, then k is equal to

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2 or -(3/2)
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-2 or - (3/2)
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2 or 3/2
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- 2 or 3/2

The centre of a circle with cuts x² + y² + 6x - 1 = 0, χ² + y² - 3y + 2 = 0 and x² + y² + x + y - 3 = 0 orthogonally, is

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0%
2)
0%
0%

tangents drawn from the point P(1,to the circle x² + y² - 6x - 4y - 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of ∆PAB is

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x2 + y2 + 4x - 6y + 19 = 0
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x2 + y2 - 4x - 10y + 19 = 0
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x2 + y2 - 2x + 6y - 29 = 0
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x2 + y2 - 6x - 4y + 19 = 0

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,for

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all values of P
0%
all except one value of p
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all except two values of p
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exactly one value of p

The number of common tangents to the circles x² + y² - y = 0 and x² + y² + y = 0 is

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2
0%
3
0%
0
0%
1

For two circles x² + y² = 16 and x² + y² - 2y = 0 there is/ are

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one pair of common tangents
0%
only one common tangent
0%
three common tangents
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no common tangent

The equation of the circle which cuts orthogonally the circle x² + y² - 6x + 4y - 3 = 0, passes through (3,and touches the y - axis, is

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x2 + y2 + 6x - 6y + 9 = 0
0%
x2 + y2 - 6x + 6y - 9 = 0
0%
x2 + y2 - 6x + 6y + 9 = 0
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None of these

If the point (3, -lies on both the circles x² + y² - 2x + 8y + 13 = 0 and x² + y² - 4x + 6y + 11 = 0, Then the angle between the circles is

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60o
0%
tan-1 (1/2)
0%
tan-1 (3/5)
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45o

Consider a family of circles, which are passing through the point (-1,and are tangent to X-axis. If (h,k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

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0 < k < 1/2
0%
K ≥ 1/2
0%
- (1/≤ k ≤ 1/2
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k ≤ 1/2

The value of k, so that x² + y² + kx + 4y + 2 = 0 and 2(x² + y²) - 4x - 3y + k = 0 cut orthogonally, is

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10/3
0%
- (8/3)
0%
-(10/3)
0%
8/3

The equations of the three circles are x² + y² - 6x - 6y + 4 = 0, x² + y² - 2x - 4y + 3 = 0 and x² + y² + 2kx + 2y + 1 = 0. If the radical centre of the above three circles exist, then which of the following cannot be the value of k?

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2
0%
1
0%
5
0%
4

The radical centre of the circles x² + y² - 16x + 60 = 0, x² + y² - 12x + 27 = 0 and x² + y² - 12y + 8 = 0 is

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(13, 33/4)
0%
(33/4, -13)
0%
(33/4, 13)
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None of these

C₁is a circle of radius 2 touching the X-axis and the Y-axis. C₂ is another circle of radius > 2 and touching the axes as well as the circle C₁. Then, the radius of C₂ is

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6 - 4√2
0%
6 + 4√2
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6 - 4√3
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6 + 4√3

If the two circles x² + 2y² - 2x + 22y + 5 = 0 and x² + y² + 14x + 6y + k = 0 intersect orthogonally, then k is equal to

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47
0%
- 47
0%
49
0%
- 49

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² - 3ax + dy - 1 = 0 intersect in two distinct points P and Q, then the line 5x + by - a = 0 passes through P and Q for

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exactly two values of a
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infinitely many values of a
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no value of a
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exactly one value of a

If a circle passes through the point (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

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2ax + 2by + (a2 + b2 += 0
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2ax + 2by - (a2 + b2 += 0
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2ax - 2by + (a2 + b2 += 0
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2ax - 2by - (a2 + b2 += 0

The shortest distance of the point (6, –from the circle x² + y² = 36, is

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4
0%
6
0%
8
0%
10

The number of feet of normals from the point (7, –to the circle x² + y² = 5 is

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1
0%
2
0%
3
0%
4

Maths-Circle and System of Circles-12543.png

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x2 + y2 + 2ax + 2by + 2b2 = 0
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x2 + y2 - 2ax - 2by - 2b2 = 0
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x2 + y2 - 2ax - 2by + 2b2 = 0
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x2 + y2 - 2ax + 2by + 2a2 = 0

The number of common tangents of the circles (x + 3)² + (y –)² = 49 and (x –)² + (y +)² = 4

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0
0%
1
0%
3
0%
4

The radius of the circle passing thro’ the point P(6, 2), two of whose diameters are x + y =6 and x + 2y = 4 is

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10
0%
2)
0%
6
0%
4

If the centroid of an equilateral triangle is (1,and its one vertex is (-1, 2), then the equation of its circumcircle is

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x2 + y2 – 2x – 2y – 3 = 0
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x2 + y2 + 2x – 2y – 3 = 0
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x2 + y2 + 2x + 2y – 3 = 0
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none of these

Two circles, each of radius 5, have a common tangent at (1,whose equation is 3x + 4y – 7 = 0 Then their centres are

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(4, –5), (–2, 3)
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(4, –3), (–2, 5)
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(4, 5), (–2, –3)
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none of these

Lines are drawn to the point P(–2, –to meet the circle x² + y² – 2x – 10y + 1 = 0. The length of the line segment PA, A being the point on the circle where the line meets the circle at coincident points, is