circles - vmkt.s3-ap-southeast-1.amazonaws.com

CIRCLES

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y − 4 x + 3 = 0, then its radius is equal to :

A B C D2 1

Solution :

11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics

A B C D6 13

A square is inscribed in the circle x2 + y2 - 6x + 8y - 103 = 0 with its sides parallel to coordinate axes.Then the distance between origin and vertex of this square which is nearest to the origin is


A square is inscribed in the circle x2 + y2 - 6x + 8y - 103 = 0 with its sides parallel to coordinate axes.Then the distance between origin and vertex of this square which is nearest to the origin is

A B C D6 13

11-01-2019 - Morning Shift - MathematicsSolution :

Equation of circle touching the lines |x - 2| + |y - 3| = 4 will be

A B

C D

(x - 2)2 + (y - 3)2 = 12 (x - 2)2 + (y - 3)2 = 4

(x - 2)2 + (y - 3)2 = 2 (x - 2)2 + (y - 3)2 = 8

Solution :

x - y = 3

The equation of the image of the circle x2 + y2 + 16x - 24y + 183 =0 in the line mirror 4x + 7y + 13 = 0 is

A B

C D

x2 + y2 + 32x - 4y + 235 = 0 x2 + y2 + 32x + 4y - 235 = 0

x2 + y2 + 32x - 4y - 235 = 0 x2 + y2 + 32x + 4y + 235 = 0

Solution :

09-01-2020-Morning Shift

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle?

A B

C D

4x – 3y + 17 = 0 3x – 4y – 24 = 0

3x + 4y – 6 = 0 4x + 3y – 8 = 0


A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle ?

A B

C D

4x – 3y + 17 = 0 3x – 4y – 24 = 0

3x + 4y – 6 = 0 4x + 3y – 8 = 0

Solution :

12-04-2019-Evening Shift

A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point :

A B C D(3, 10) (3, 5) (2, 3) (1, 5)

Solution :


The sum of the squares of the lengths of the chords intercepted on the circle, x2 + y2 = 16, by the lines, x + y = n, n ∈ N, where N is the set of all natural numbers, is :

Solution :

The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point

(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is ..

A B C D2 3


(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is ..


(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is :

A B C D2 3

Solution :


The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

A B C D

11-01-2019 - Morning Shift - MathematicsSolution :


If a line, y = mx + c is a tangent to the circle, ( x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ; then

A B

C D

c2 + 7c + 6 = 0 c2 + 6c + 7 = 0

c2 – 6c + 7 = 0 c2 – 7c + 6 = 0


If a line, y = mx + c is a tangent to the circle, ( x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ; then :

A B

C D

c2 + 7c + 6 = 0 c2 + 6c + 7 = 0

c2 – 6c + 7 = 0 c2 – 7c + 6 = 0

Solution :


The tangent and the normal lines at the point to the circle x2 + y2 = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :

A B C D

Solution :


A B

C D

The locus of the centres of the circles, which touch the circle x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is:


The locus of the centres of the circles, which touch the circle x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is:

A B

C D

Solution :

The locus of the centre of a circle which touches externally the circle (x - 3)2 + (y - 3)2 = 4 and also touches the y-axis is given by the equation:

A B

C D

x2 - 6x - 10y + 14 = 0 x2 - 10x - 6y + 14 = 0

y2 - 6x - 10y + 14 = 0 y2 - 10x - 6y + 14 = 0

Solution :


If the curves, x2 - 6x + y2 + 8 = 0 and x2 - 8y + y2 + 16 - k =0, (k > 0) touch each other at a point, then the largest value of k is

Solution :


If the circles x2 + y2 – l6x – 20y + 164 = r2 and (x – 4)2 + (y – 7)2 =36 intersect at two distinct points, then:

A B C Dr > 11 0 < r < 1 r = 11 1 < r < 11

Solution :

Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle when

A B

C D

All are integral values of K 0 < K < 1

K < 0 For two values of K

Solution :

If a circle passes through the points of intersection of the coordinate axes with the lines λx - y + 1 = 0 and x - 2y + 3 = 0, then the value of λ is

A B C D2 4 6 3

Solution :

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

A B

C D

x2 + y2 + x + y = 0 x2 + y2 - x - y = 0

x2 + y2 + x - y = 0 None of these

Solution :


The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is:

A B C D3 2

Solution :

12-01-2019 - Morning Shift12-01-2019-Morning Shift

Let C1 and C2 be centres of the circles x2 + y2 -2x - 2y – 2 = 0 and x2 + y2- 6x - 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles then, area (in sq. units) of the quadrilateral PC1QC2 is : ______

A B C D8 6 9 4

12-01-2019 - Morning Shift

Solution :


If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for..

A

B

C

D

Infinitely many values of K

No value of K.

Exactly two values of K

Exactly one value of K


If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for..


If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for:

A

B

C

D

Infinitely many values of K

No value of K.

Exactly two values of K

Exactly one value of K

Solution :


Let the tangents drawn from the origin to the circle, x2 + y2 – 8x – 4y + 16 = 0 touch it at the point A and B. Then (AB)2 is equal to:

A B C D

Solution :


If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :

A B C D

Solution :

From origin, chords are drawn to the circle x2 + y2 - 2y = 0. The locus of the middle points of these chords is

A B

C D

x2 + y2 - y = 0 x2 + y2 - x = 0

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

Solution :

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