Circle and System of Circles Test

Result

Circle and System of Circles Test - 7

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Weekly Quiz Competition

Question 1
4 / -1

The radius of the circle x² + y² + 4x + 6y + 13 = 0 is

A
√26

B
√13

C
√23

D
0
Question 2
4 / -1

If x - y + 1 = 0 meets the circle x² + y² + y - 1 = 0 at A and b, then the equation of the circle wit AB as diameter, is

A
2(x² + y²) + 3x - y + 1 = 0

B
2(x² + y²) + 3x - y + 2 = 0

C
2(x² + y²) + 3x - y + 3 = 0

D
x² + y² + 3x - y + 1 = 0
Question 3
4 / -1

Which of the following equations given circle ?

A
r = 2 sin θ

B
r² cos 2θ = 1

C
r( 4 cos θ + 5 sin θ) = 3

D
5 = r (1 + √2 cos θ)
Question 4
4 / -1

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed numbeer (≠ 1). Then, its locus is a

A
parabola

B
circle

C
hyperbola

D
pair of straight lines
Question 5
4 / -1

The circles x² + y² + 4x - 4y + 4 = 0 touches

A
X - axis

B
Y - axis

C
X - axis and Y - axis

D
None of these
Question 6
4 / -1

If a > 2b > 0, then positive value of m for which y = mx - b√(1 + m) is a common tangent x² + y² = b² and (x - a)² + y² = b², is

A

B

C

D
Question 7
4 / -1

The equation of the two tangents from (-5, -4) to the circle x² + y² + 4x + 6y + 8 = 0 are

A
x + 2y + 13 = 0, 2x - y + 6 = 0

B
2x + y + 13 = 0, x - 2y = 6

C
3x + 2y + 23 = 0, 2x - 3y + 4 = 0

D
x - 7y = 23, 6x + 13y = 4
Question 8
4 / -1

The length (in units) of tangent from point (5, 1) to the circle x² + y² + 6x - 4y - 3 = 0 is

A
81

B
29

C
7

D
21

Solution
Question 9
4 / -1

Circle ax² + ay² + 2gx + 2fy + c = 0 touches X - axis, if

A
f² > ac

B
g² > ac

C
f² = bc

D
g² = ac
Question 10
4 / -1

The equation of normal of x² + y² - 2x + 4y - 5 = 0 at (2, 1) is

A
y = 3x - 5

B
2y = 3x - 4

C
y = 3x + 4

D
y = x + 1