Circle and System of Circles Test

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Circle and System of Circles Test - 16

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Weekly Quiz Competition

Question 1
4 / -1

The equation of circle which touches the lines x = y at origin and passes through the point (2, 1) is x² + y² + px + qy = 0. Then, p, q are

A
-5, 5

B
-5, 5

C
5, - 5

D
None of these
Question 2
4 / -1

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

A
4π

B
3π

C
2π

D
π

Solution
Question 3
4 / -1

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

A
x² + y² ± 4x ± 8y = 0

B
x² + y² ± 2x ± 4y = 0

C
x² + y² ± 8x ± 16y = 0

D
x² + y² ± x ± y = 0
Question 4
4 / -1

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

A
y² + 6x = 0

B
y² + 6x = 13

C
y² + 6x = 10

D
x² + 6y = 13
Question 5
4 / -1

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

A
x² + y² - 4x - 6y - 16 = 0

B
x² + y² - 4x - 6y - 20 = 0

C
x² + y² - 4x - 6y - 12 = 0

D
x² + y² + 4x + 6y - 12 = 0
Question 6
4 / -1

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

A
x² + y² - 4y + 3 = 0

B
x² + y² - 2y - 2 = 0

C
x² + y² - 2x - 2y + 2 = 0

D
x² + y² - 2x - 2y + 1 = 0
Question 7
4 / -1

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

A
√11/3

B
√13/3

C
√7/3

D
1/3

Solution
Question 8
4 / -1

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

A
4

B
2√5

C
5

D
3√5
Question 9
4 / -1

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

A
(3, 4)

B
(3, - 4)

C
(-3, 4)

D
(-3, - 4)
Question 10
4 / -1

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

A
8

B
7

C
6

D
5

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Circle and System of Circles Test - 16

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Circle and System of Circles Test - 16

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Question 1

-5, 5

-5, 5

5, - 5

None of these

Question 2

4π

3π

2π

π

Solution

Question 3

x2 + y2 ± 4x ± 8y = 0

x2 + y2 ± 2x ± 4y = 0

x2 + y2 ± 8x ± 16y = 0

x2 + y2 ± x ± y = 0

Question 4

y2 + 6x = 0

y2 + 6x = 13

y2 + 6x = 10

x2 + 6y = 13

Question 5

x2 + y2 - 4x - 6y - 16 = 0

x2 + y2 - 4x - 6y - 20 = 0

x2 + y2 - 4x - 6y - 12 = 0

x2 + y2 + 4x + 6y - 12 = 0

Question 6

x2 + y2 - 4y + 3 = 0

x2 + y2 - 2y - 2 = 0

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

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

Question 7

√11/3

√13/3

√7/3

1/3

Solution

Question 8

4

2√5

5

3√5

Question 9

(3, 4)

(3, - 4)

(-3, 4)

(-3, - 4)

Question 10

8

7

6

5

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x² + y² ± 4x ± 8y = 0

x² + y² ± 2x ± 4y = 0

x² + y² ± 8x ± 16y = 0

x² + y² ± x ± y = 0

y² + 6x = 0

y² + 6x = 13

y² + 6x = 10

x² + 6y = 13

x² + y² - 4x - 6y - 16 = 0

x² + y² - 4x - 6y - 20 = 0

x² + y² - 4x - 6y - 12 = 0

x² + y² + 4x + 6y - 12 = 0

x² + y² - 4y + 3 = 0

x² + y² - 2y - 2 = 0

x² + y² - 2x - 2y + 2 = 0

x² + y² - 2x - 2y + 1 = 0