JEE Questions for Maths Circle And System Of Circles Quiz 3

A square is inscribed in the circle x² + y² – 2x + 4y + 3 = 0. Its sides are parallel to the coordinate axes. The one vertex of the square is

0%
0%
2)
0%
0%
none of these

Compute the shortest distance between the circle x² + y² - 10x - 14y - 151 = 0 and the point (-7, 2).

0%
0
0%
1
0%
2
0%
4

The centre of the circle passing through the point (0,and touching the curve y = x² at (2,is

0%
0%
2)
0%
0%
none of these

The circle passing through (1, -and touching the X-axis at (3, 0), also passes through the point

0%
(-5, 2)
0%
(2, -5)
0%
(5, - 2)
0%
(-2, 5)

If the equation of the tangent to the circle x² + y² - 2x + 6y - 6 = 0 parallel to 3x - 4y + 7 = 0 is 3x - 4y + k = 0, then the values of k are

0%
5, -35
0%
-5, 35
0%
7, - 32
0%
-7, 32
0%
None of these

Circles are drawn through the point (2,to cut intercept of length 5 units on the X-axis. If their centres lies in the first quadrant, then their equation is

0%
x2 + y2 - 9x + 2fy + 14 = 0
0%
3x2 + 3y2 + 27x - 2fy + 42 = 0
0%
x2 + y2 - 9x - 2fy + 14 = 0
0%
x2 + y2 - 2fx - 9y + 14 = 0

Two vertices of a equilateral triangle are (-1,and (1,and its circumcircle is

0%
0%
2)
0%
0%
None of these

The line 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle of area 154 sq units. Then, the equation of the circle is

0%
x2 + y2 - 2x + 2y + 47 = 0
0%
x2 + y2 + 2x - 2y - 47 = 0
0%
x2 + y2 - 2x + 2y - 47 = 0
0%
x2 + y2 - 2x - 2y - 47 = 0

The length of the diameter of the circle which touches the X- axis at the point (1,and passes through the point (2,is

0%
10/3
0%
3/5
0%
6/5
0%
5/3

The least and the greatest distance of the point(10,from the circle x² + y² - 4x - 2y - 20 = 0 are

0%
10, 5
0%
15, 20
0%
12, 16
0%
5, 15

The equation of the circle passing through (1,and the points of intersection of x² + y² + 13x – 3y = 0 and 2x² + 2y² + 4x – 7y – 25 = 0 is

0%
4x2 + 4y2 – 30x – 10y – 25 = 0
0%
4x2 + 4y2 + 30x – 13y – 25 = 0
0%
4x2 + 4y2 – 17x – 10y + 25 = 0
0%
none of these

The circle passing through the point(-1,and touching the Y - axis at (0, 2), also passes through the point

0%
(-(3/2), 0)
0%
(-(5/2), 2)
0%
(-(3/2), 5/2)
0%
(-4, 0)

The intercept on the line y = x by the circle x² + y² - 2x = 0 is AB. Equation of the circle with AB as diameter is

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

The circle x² + y² = 4x + 8y + 5 intersects the line 3x - 4y = m at two distinct points, if

0%
-85 < m < - 35
0%
-35 < m < 15
0%
15 < m < 65
0%
35 < m < 85

The line segment joining points (4,and (-2, -is a diameter of a circle. If the circle intersects the X - axis at A and B, then AB is equal to

0%
4
0%
5
0%
6
0%
8

The distance of the mid-point of line joining two points (4,and (0,from the center of the circle x² + y² = 16 is

0%
√2
0%
2√2
0%
3√2
0%
2√3

The equation of family of circles with centre at (h, k) touching the X-axis is given by

0%
x2 + y2 - 2hx + h2 = 0
0%
x2 + y2 - 2hx - 2ky + h2 = 0
0%
x2 + y2 - 2hx - 2ky - h2 = 0
0%
x2 + y2 + 2hx + 2ky = 0
0%
x2 + y2 + 2hx + 2ky = 0

The straight line x + y - 1 = 0 meets the circle x² + y² - 6x - 8y = 0 at A and B. Then, the equation of the circle of which AB is a diameter, is

0%
x2 + y2 - 2y - 6 = 0
0%
x2 + y2 + 2y - 6 = 0
0%
2(x2 + y- 2y - 6 = 0
0%
3(x2 + y+ 2y - 6 = 0

If a circle passes through (0, 0), (a,and (0, b), then the coordinates of its centre are

0%
(b/2, a/2)
0%
(a/2, b/2)
0%
(b, a)
0%
(a, b)

The coordinates of the centre of the smallest circle passing through the origin and having y = x + 1 as a diameter, are

0%
(1/2, - (1/2))
0%
(1/2, 1/3)
0%
(-1, 0)
0%
(-(1/2), 1/2)

The equation of circle which touches the lines x = y at origin and passes through the point (2,is x² + y² + px + qy = 0. Then, p, q are

0%
-5, 5
0%
-5, 5
0%
5, - 5
0%
None of these

The area (in sq units) of the circle which touches the lines 4x + 3y = 15 and 4x + 3y = 5 is

0%
4π
0%
3π
0%
2π
0%
π

The equations of the circle which pass through the origin and make intercepts of lengths 4 and 8 on the X and Y - axes respectively, are

0%
x2 + y2 ± 4x ± 8y = 0
0%
x2 + y2 ± 2x ± 4y = 0
0%
x2 + y2 ± 8x ± 16y = 0
0%
x2 + y2 ± x ± y = 0

The locus of center of a circle which passes through the origin and cut off a length of 4 units from the line x = 3 is

0%
y2 + 6x = 0
0%
y2 + 6x = 13
0%
y2 + 6x = 10
0%
x2 + 6y = 13

The diameters of a circle are along 2x + y - 7 = 0 and x + 3y - 11 = 0. Then, the equation of this circle, which also passes through (5, 7), is

0%
x2 + y2 - 4x - 6y - 16 = 0
0%
x2 + y2 - 4x - 6y - 20 = 0
0%
x2 + y2 - 4x - 6y - 12 = 0
0%
x2 + y2 + 4x + 6y - 12 = 0

The equation of circle which touches X and Y - axes at the points (1,and (0,respectively is

0%
x2 + y2 - 4y + 3 = 0
0%
x2 + y2 - 2y - 2 = 0
0%
x2 + y2 - 2x - 2y + 2 = 0
0%
x2 + y2 - 2x - 2y + 1 = 0

If the equation λx² + (2λ - 3)y² - 4x - 1 = 0 represents a circle, then its radius is

0%
√11/3
0%
√13/3
0%
√7/3
0%
1/3

If the tangent at point P on the circle x² + y² + 6x + 6y - 2 = 0 meets the straight line 5x - 2y + 6 = 0 at a point Q on y - axis, the length of PQ is

0%
4
0%
2√5
0%
5
0%
3√5

The point diametrically opposite to the point P(1,on the circle x² + y² + 2x + 4y - 3 = 0 is

0%
(3, 4)
0%
(3, - 4)
0%
(-3, 4)
0%
(-3, - 4)

The radius of the circle with the polar equation r² - 8r(√3 cos θ + sin θ) + 15 = 0 is

0%
8
0%
7
0%
6
0%
5

If the lines 2x - 3y = 5 and 3x - 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is

0%
x2 + y2 + 2x - 4y - 47 = 0
0%
x2 + y2 = 49
0%
x2 + y2 - 2x + 2y - 47 = 0
0%
x2 + y2 = 17

The circle x² + y² - 4x - 4y + 4 = 0 is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is x + y - xy + k √(x² + y²) = 0, then the value of k is

0%
2
0%
1
0%
- 2
0%
3

If one end of the diameter is (1,and the other end lies on the line x + y = 3, then locus of centre of circle is

0%
x+ y = 1
0%
2(x - y ) = 5
0%
2x + 2y = 5
0%
None of these

The equation of the smallest circle passing through the points (2,and (3,is

0%
x2 + y2 + 5x + 5y + 12 = 0
0%
x2 + y2 - 5x - 5y + 12 = 0
0%
x2 + y2 + 5x - 5y + 12 = 0
0%
x2 + y2 - 5x + 5y - 12 = 0

The equation (x - x₁) (x - x₂) + (y - y₁) ( y - y₂) = 0 represents a circle whose centre is

0%
0%
2)
0%
(x1, y1)
0%
(x2, y2)

The center of the circle whose normals are x² - 2xy - 3x + 6y = 0, is

0%
0%
2)
0%
0%
None of these

The equation of the circle with center (2,and touching the line 3x + 4y = 5 is

0%
x2 + y2 - 4x - 2y + 5 = 0
0%
x2 + y2 - 4x - 2y - 5 = 0
0%
x2 + y2 - 4x - 2y + 4 = 0
0%
x2 + y2 - 4x - 2y - 4 = 0

If 2x - 4y = 9 and 6x - 12y + 7 = 0 are common tangents to the circle, then radius of circle is

0%
√3/5
0%
17/6√5
0%
√2/3
0%
17/3√5

If P(x₁, y₁) and Q(x₂, y₂) are two pints such that their abscissae x₁ and x₂ are the roots of the equation x² + 2x - 3 = 0 while the ordinates y₁ and y₂ are the roots of the equation y² + 4y - 12 = 0. Then, the centre of the circle wit PQ as diameter is

0%
(-1, - 2)
0%
(1, 2)
0%
(1, -2)
0%
(-1,2)

The locus of the centre of the circle for which one end of a diameter is (1,while the other end is in the line x + y = 3 is

0%
x+ y = 1
0%
2(x - y) = 5
0%
2x + 2y = 5
0%
None of these

A tangent PT is drawn to the circle x² + y² = 4 at the point P(√3, 1). A straight line L, perpendicular to PT is a tangent to the circle (x - 3)² + y² = 1
A common tangent of the two circle is

0%
x = 4
0%
y = 2
0%
x + √3y = 4
0%
x + 2√2y = -6

A tangent PT is drawn to the circle χ² + y² = 4 at the point P(√3, 1). A straight line L, perpendicular to PT is a tangent to the circle (χ - 3)² + y² = 1
A possible equation L is

0%
χ - √3 y = 1
0%
y = 2
0%
χ + √3 y = -1
0%
χ + √3 y = 5

The equation of the tangent from the point (0,to the circle x² + y² - 2x - 6y + 6 = 0, is

0%
y - 1 = 0
0%
4x + 3y + 3 = 0
0%
4x - 3y - 3 = 0
0%
y + 1 = 0

If m₁ and m₂ are the slopes of tangents to the circle x² + y² = 4 from the point (3, 2), then m₁ - m₂ is equal to

0%
5/12
0%
12/5
0%
3/2
0%
0

The angle between the tangents dawn at the points (5,and (12, -to the circles x² + y² = 169 is

0%
45o
0%
60o
0%
30o
0%
9045o

Tangents are drawn from the point (17,to the circle x² + y² = 169²
Statement I The tangents are mutually perpendicular
Statement II The locus of the points from which mutually perpendicular tangents can be drawn to the given circles is x² + y² = 338

0%
Statement I is correct, Statement Ii is correct; Statement II is correct explanation for Statement I
0%
Statement t I is a correct, Statement II is correct; Statement II is not a correct explanation for Statement I
0%
Statement I is correct, Statement II is correct
0%
Statement I is incorrect, Statement II is correct

If 3x + y + k = 0 is a tangent to the circle x² + y² = 10, then the values of k are

0%
± 7
0%
± 5
0%
± 10
0%
± 9

From the point P(16, 7), tangents PQ and PR are drawn to circle x² + y² - 2x - 4y - 20 = 0. If C is the centre of the circle, then area of equilateral PQCR is

0%
450 sq units
0%
15 sq units
0%
50 sq units
0%
75 sq units

The condition for a line y = 2x + c to touch the circle x + y² = 16 is

0%
c = 10
0%
c2 = 80
0%
c = 12
0%
c2 = 64

The equation of the common tangent of the two touching circles, y² + x² - 6x -12y + 37 = 0 and x² + y² - 6y + 7 = 0 is

0%
x + y - 5 = 0
0%
x - y + 5 = 0
0%
x - y - 5 = 0
0%
x + y + 5 = 0

JEE Questions for Maths Circle And System Of Circles Quiz 3 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

JEE Questions for Maths Circle And System Of Circles Quiz 3 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

Support mcqexams.com by disabling your adblocker.