>> Elementary Mathematics >> Circles
1). The square of the length of the tangent from \( \Large \left(3,\ -4\right) \) to the circle \( \Large x^{2}+y^{2}-4x-6y+3=0 \) is:
A). 20 B). 30
C). 40 D). 50
2). 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
3). 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). \( \Large \pi R^{2} \)
4). 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). \( \Large \frac{5}{2} \)
5). 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
6). 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
7). 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). \( \Large \left(1,\ -4\right) \)
8). 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). \( \Large \sqrt{20} \)
9). 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
10). 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). \( \Large x+y=x^{2}_{1}+y^{2}_{1} \)