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If \( \Large g^{2}+f^{2}=c \) then the equation \( \Large x^{2}+y^{2}+2gx+2fy+c=0 \) will represent:

A) a Circle of radius g
B) a circle of radius f
C) a circle of diameter \( \Large \sqrt{c} \)
D) a circle of radius 0

Correct Answer:




D) a circle of radius 0

Description for Correct answer:
Given that \( \Large x^{2}+y^{2}+2gx+2fy+c=0 \)

and \( \Large g^{2}+f^{2}=c \)

Radius of circle = \( \Large \sqrt{g^{2}+f^{2}-c} \)

\( \Large \therefore g^{2}+f^{2}=c \)

=> Radius = 0

Thus given equation represents a circle of radius 0.

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

Comments

Similar Questions

1). The limit of the perimeter of the regular n polygons inscribe in a circle of radius R as \( \Large n\ \rightarrow\ \infty \) is:

A). \( \Large 2 \pi R \)

B). \( \Large \pi R \)

C). \( \Large 4R \)

D). \( \Large \pi R^{2} \)

2). The value of n, for which the circle \( \Large x^{2}+y^{2}+2nx+6y+1=0 \) intersects the circle \( \Large x^{2}+y^{2}+4x+2y=0 \) orthogonally is:

A). \( \Large \frac{11}{8} \)

B). -1

C). \( \Large \frac{-5}{4} \)

D). \( \Large \frac{5}{2} \)

3). The Value of c for which the line \( \Large y=2x+c \) is a tangent to the circle \( \Large x^{2}+y^{2}=16 \) is:

A). \( \Large -16\sqrt{5} \)

B). \( \Large 4\sqrt{5} \)

C). \( \Large 16\sqrt{5} \)

D). 20

4). 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

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

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

7). 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

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

9). 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 \( \Large 4x+3y+12=0 \)

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