Circle and System of Circles Test

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Circle and System of Circles Test - 13

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Weekly Quiz Competition

Question 1
4 / -1

If (-3, 2) lies on the circle x² + y² + 2gx + 2fy + c = 0 which is concentric with the circle x² + y² + 6x + 8y - 5 = 0, then c is equal to

A
11

B
- 11

C
24

D
100
Question 2
4 / -1

The condition for the coaxial system x² + y² + 2λx + c = 0, where λ is a parameter and c is a constant to have distinct limiting points, is

A
c = 0

B
c < 0

C
c = -1

D
c > 0
Question 3
4 / -1

If the radical axis of the circles x² + y² + 2gx + 2fy + c = 0 and 2x² + 2y² + 3x + 8y + 2c = 0, touches the circle x² + y² + 2x + 2y + 1 = 0, then

A
g = 3/4 anf f ≠ 2

B
g ≠ 3/4 anf f = 2

C
g = 3/4 and f = 2

D
None of these
Question 4
4 / -1

The two circles x² + y² - 5 = 0 and x² + y² - 2x - 4y - 15 = 0

A
touch each other externally

B
touch each other internally

C
cut each other orthogonally

D
do not intersect
Question 5
4 / -1

The two circles x² + y² - 2x + 6y + 6 = 0 and x² + y² - 5x + 6y + 15 = 0 touch each other

A
externally

B
internally

C
coincide

D
None of these
Question 6
4 / -1

The circles x² + y² - 10x + 16 = 0 and x² + y² = r intersect each other at two distinct points, if

A
r < 2

B
r4 > 8

C
2 < r < 8

D
2 ≤ r ≤ 8
Question 7
4 / -1

The radical axis of the coaxial system of circles with limiting points (1, 2) and (- 2,1) is

A
x+ 3y = 0

B
3x + y = 0

C
2x + 3y = 0

D
3x + 2y = 0
Question 8
4 / -1

The number of common tangents to circles x² + y² + 2x + 8y - 23 = 0 and x² + y² - 4x - 10y + 9 = 0, is/are

A
1

B
3

C
2

D
None of these
Question 9
4 / -1

If the circles x² + y² + 2gx + 2fy = 0 and x² + y² + 2g\'x + 2f \' y = 0 touch each other, than

A
ff ' = gg'

B
fg = f ' g'

C
(fg)² = (f ' g ')²

D
fg' = f ' g
Question 10
4 / -1

If two circles of the same radius r and centres at (2. 3) and (5, 6) respectively cut orthogonally, then the value of r is

A
3

B
2

C
1

D
5

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Circle and System of Circles Test - 13

Result

Circle and System of Circles Test - 13

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SHARING IS CARING

Question 1

11

- 11

24

100

Question 2

c = 0

c < 0

c = -1

c > 0

Question 3

g = 3/4 anf f ≠ 2

g ≠ 3/4 anf f = 2

g = 3/4 and f = 2

None of these

Question 4

touch each other externally

touch each other internally

cut each other orthogonally

do not intersect

Question 5

externally

internally

coincide

None of these

Question 6

r < 2

r4 > 8

2 < r < 8

2 ≤ r ≤ 8

Question 7

x+ 3y = 0

3x + y = 0

2x + 3y = 0

3x + 2y = 0

Question 8

1

3

2

None of these

Question 9

ff ' = gg'

fg = f ' g'

(fg)2 = (f ' g ')2

fg' = f ' g

Question 10

3

2

1

5

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(fg)² = (f ' g ')²