Circle and System of Circles Test

Result

Circle and System of Circles Test - 17

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

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

A
x² + y² + 2x - 4y - 47 = 0

B
x² + y² = 49

C
x² + y² - 2x + 2y - 47 = 0

D
x² + y² = 17
Question 2
4 / -1

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

A
2

B
1

C
- 2

D
3
Question 3
4 / -1

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

A
x+ y = 1

B
2(x - y ) = 5

C
2x + 2y = 5

D
None of these
Question 4
4 / -1

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

A
x² + y² + 5x + 5y + 12 = 0

B
x² + y² - 5x - 5y + 12 = 0

C
x² + y² + 5x - 5y + 12 = 0

D
x² + y² - 5x + 5y - 12 = 0

Solution
Question 5
4 / -1

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

A

B

C
(x₁, y₁)

D
(x₂, y₂)
Question 6
4 / -1

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

A

B

C

D
None of these
Question 7
4 / -1

The equation of the circle with center (2, 1) and touching the line 3x + 4y = 5 is

A
x² + y² - 4x - 2y + 5 = 0

B
x² + y² - 4x - 2y - 5 = 0

C
x² + y² - 4x - 2y + 4 = 0

D
x² + y² - 4x - 2y - 4 = 0
Question 8
4 / -1

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

A
√3/5

B
17/6√5

C
√2/3

D
17/3√5
Question 9
4 / -1

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

A
(-1, - 2)

B
(1, 2)

C
(1, -2)

D
(-1,2)
Question 10
4 / -1

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

A
x+ y = 1

B
2(x - y) = 5

C
2x + 2y = 5

D
None of these