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The radical axis of two circle and line joining their centres are:

A) Parallel
B) Perpendicular
C) Neither Parallel nor perpendicular
D) Intersecting but not perpendicular

Correct Answer:


B) Perpendicular

Description for Correct answer:
Radical axis is the common chord of the two circles and radical axis is perpendicular to the line joining the centers of two circles.

Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles

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Similar Questions

1). Which of the following is a point on the common chord of the circles \( \Large x^{2}+y^{2}+2x-3y+6=0\ and\ x^{2}+y^{2}+x-8y-13=0 \)?

A). \( \Large \left(1,\ -2 \right) \)

B). \( \Large \left(1,\ 4\right) \)

C). \( \Large 1,\ 2 \)

D). \( \Large \left(1,\ -4\right) \)

2). The radius of the circle passing through the point \( \Large \left(6,\ 2\right) \) and two of whose diameter are \( \Large x+y=6\ and\ x+2y=4 \) is:

A). 4

B). 6

C). 20

D). \( \Large \sqrt{20} \)

3). The radius of any circle touching the lines \( \Large 3x-4y+5=0\ and\ 6x-8y-9=0 \) is:

A). 1.9

B). 0.95

C). 2.9

D). 1.45

4). The locus of the middle point of the chords of the circle \( \Large x^{2}+y^{2}=a^{2} \) such that the chords pass through a given point \( \Large \left(x_{1},\ y_{1}\right) \) is:

A). \( \Large x^{2}+y^{2}-xx_{1}-yy_{1}=0 \)

B). \( \Large x^{2}+y^{2}=x^{2}_{1}+y^{2}_{1} \)

C). \( \Large x+y=x_{1}+y'_{2} \)

D). \( \Large x+y=x^{2}_{1}+y^{2}_{1} \)

5). The equations of the tangents to the circle \( \Large x^{2}+y^{2}-6x+4y-12=0 \) which are parallel to the line \( \Large 4x+3y+5=0 \),are

A). \( \Large 4x+3y+11=0 \) and \( \Large 4x+3y+8=0 \)

B). \( \Large 4x+3y-9=0 \) and \( \Large 4x+3y+7=0 \)

C). \( \Large 4x+3y+19=0 \) and \( \Large 4x+3y-31=0 \)

D). \( \Large 4x+3y-10=0 \) and \( \Large 4x+3y+12=0 \)

6). The lines \( \Large 2x-3y=5\ and\ 3x-4y=7 \) are diameters of a circle having area as 154 sq unit. Then the equation of the circle is:

A). \( \Large x^{2}+y^{2}+2x-2y=62 \)

B). \( \Large x^{2}+y^{2}+2x-2y=47 \)

C). \( \Large x^{2}+y^{2}-2x+2y=47 \)

D). \( \Large x^{2}+y^{2}-2x+2y=62 \)

7). The pole of the straight line \( \Large x+2y=1 \) with respect to the circle \( \Large x^{2}+y^{2}=5 \) is:

A). \( \Large \left(5,\ 5\right) \)

B). \( \Large \left(5,\ 10\right) \)

C). \( \Large \left(10,\ 5\right) \)

D). \( \Large \left(10,\ 10\right) \)

8). If the circle \( \Large x^{2}+y^{2}+6x-2y+k=0 \) bisects the circumference of the circle \( \Large x^{2}+y^{2}+2x-6y-15=0 \) then k is equal to:

A). 21

B). -21

C). 23

D). -23

9). If \( \Large 5x-12y=10 \) and \( \Large 12y-5x+16=0 \) are two tangents to a circle, then the radius of the circle is

A). 1

B). 2

C). 4

D). 6

10). Equation of the circle passing through the point \( \Large \left(3,\ 4\right) \) and concentric with the circle \( \Large x^{2}+y^{2}-2x-4y+1=0 \) is

A). \( \Large x^{2}+y^{2}-2x-4y=0 \)

B). \( \Large x^{2}+y^{2}-2x-4y+3=0 \)

C). \( \Large x^{2}+y^{2}-2x-4y-3=0 \)

D). none of the above