Topics

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