Circle and System of Circles Test

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Circle and System of Circles Test - 21

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Weekly Quiz Competition

Question 1
4 / -1

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

A
all values of P

B
all except one value of p

C
all except two values of p

D
exactly one value of p

Solution
Question 2
4 / -1

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

A
2

B
3

C
0

D
1

Solution
Question 3
4 / -1

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

A
one pair of common tangents

B
only one common tangent

C
three common tangents

D
no common tangent
Question 4
4 / -1

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

A
x² + y² + 6x - 6y + 9 = 0

B
x² + y² - 6x + 6y - 9 = 0

C
x² + y² - 6x + 6y + 9 = 0

D
None of these
Question 5
4 / -1

If the point (3, - 4) 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

A
60^o

B
tan^-1 (1/2)

C
tan^-1 (3/5)

D
45^o
Question 6
4 / -1

Consider a family of circles, which are passing through the point (-1,1) 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

A
0 < k < 1/2

B
K ≥ 1/2

C
- (1/2) ≤ k ≤ 1/2

D
k ≤ 1/2
Question 7
4 / -1

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

A
10/3

B
- (8/3)

C
-(10/3)

D
8/3
Question 8
4 / -1

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?

A
2

B
1

C
5

D
4
Question 9
4 / -1

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

A
(13, 33/4)

B
(33/4, -13)

C
(33/4, 13)

D
None of these
Question 10
4 / -1

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

A
6 - 4√2

B
6 + 4√2

C
6 - 4√3

D
6 + 4√3

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Re-Attempt Weekly Quiz Competition

Circle and System of Circles Test - 21

Result

Circle and System of Circles Test - 21

Score

-

Rank

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SHARING IS CARING

Question 1

all values of P

all except one value of p

all except two values of p

exactly one value of p

Solution

Question 2

2

3

0

1

Solution

Question 3

one pair of common tangents

only one common tangent

three common tangents

no common tangent

Question 4

x2 + y2 + 6x - 6y + 9 = 0

x2 + y2 - 6x + 6y - 9 = 0

x2 + y2 - 6x + 6y + 9 = 0

None of these

Question 5

60o

tan-1 (1/2)

tan-1 (3/5)

45o

Question 6

0 < k < 1/2

K ≥ 1/2

- (1/2) ≤ k ≤ 1/2

k ≤ 1/2

Question 7

10/3

- (8/3)

-(10/3)

8/3

Question 8

2

1

5

4

Question 9

(13, 33/4)

(33/4, -13)

(33/4, 13)

None of these

Question 10

6 - 4√2

6 + 4√2

6 - 4√3

6 + 4√3

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x² + y² + 6x - 6y + 9 = 0

x² + y² - 6x + 6y - 9 = 0

x² + y² - 6x + 6y + 9 = 0

60^o

tan^-1 (1/2)

tan^-1 (3/5)

45^o