Circle and System of Circles Test

Result

Circle and System of Circles Test - 22

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Weekly Quiz Competition

Question 1
4 / -1

If the two circles x² + 2y² - 2x + 22y + 5 = 0 and x² + y² + 14x + 6y + k = 0 intersect orthogonally, then k is equal to

A
47

B
- 47

C
49

D
- 49

Solution
Question 2
4 / -1

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² - 3ax + dy - 1 = 0 intersect in two distinct points P and Q, then the line 5x + by - a = 0 passes through P and Q for

A
exactly two values of a

B
infinitely many values of a

C
no value of a

D
exactly one value of a
Question 3
4 / -1

If a circle passes through the point (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

A
2ax + 2by + (a² + b² + 4) = 0

B
2ax + 2by - (a² + b² + 4) = 0

C
2ax - 2by + (a² + b² + 4) = 0

D
2ax - 2by - (a² + b² + 4) = 0
Question 4
4 / -1

The shortest distance of the point (6, –8) from the circle x² + y² = 36, is

A
4

B
6

C
8

D
10

Solution
Question 5
4 / -1

The number of feet of normals from the point (7, –4) to the circle x² + y² = 5 is

A
1

B
2

C
3

D
4

Solution
Question 6
4 / -1

A
x² + y² + 2ax + 2by + 2b² = 0

B
x² + y² - 2ax - 2by - 2b² = 0

C
x² + y² - 2ax - 2by + 2b² = 0

D
x² + y² - 2ax + 2by + 2a² = 0

Solution
Question 7
4 / -1

The number of common tangents of the circles (x + 3)² + (y – 2) )² = 49 and (x – 2) )² + (y + 1) )² = 4

A
0

B
1

C
3

D
4

Solution
Question 8
4 / -1

The radius of the circle passing thro’ the point P(6, 2), two of whose diameters are x + y =6 and x + 2y = 4 is

A
10

B

C
6

D
4

Solution
Question 9
4 / -1

If the centroid of an equilateral triangle is (1, 1) and its one vertex is (-1, 2), then the equation of its circumcircle is

A
x² + y² – 2x – 2y – 3 = 0

B
x² + y² + 2x – 2y – 3 = 0

C
x² + y² + 2x + 2y – 3 = 0

D
none of these

Solution
Question 10
4 / -1

Two circles, each of radius 5, have a common tangent at (1,1) whose equation is 3x + 4y – 7 = 0 Then their centres are

A
(4, –5), (–2, 3)

B
(4, –3), (–2, 5)

C
(4, 5), (–2, –3)

D
none of these

Solution