Definition of Circle

Q. The equation of the circumcircle of the triangle formed by the lines $y+\sqrt{3}x=6,y-\sqrt{3}x=6,$ and $y=0,$ is

1. $x^2+y^2-4y=0$
2. $x^2+y^2+4x=0$
3. $x^2+y^2-4y=12$
4. $x^2+y^2+4x=12$

Q. The area of a circle whose centre is (h, k) and radius a is

1. $\pi (h^2+k^2-a^2)$
2. $\pi (a^{2}hk$
3. $\pi (a^2$
4. None of these

Q. Solve: $1-3m+\frac{9m(m-1)}{2}=559$

Q. Show that the lines $\sqrt{3x}-y=2$, $\sqrt{3x}-y+1=0$ and $y=0$ are the side of an equilateral triangle.

Q.

The values of $\lambda$ for which the circle $x^2+y^2+6x+5+\lambda (x^2+y^2-8x+7)=0$ dwindles into a point are

1. $2\pm \frac{2\sqrt{2}}{3}$
   

2. $1\pm \frac{\sqrt{2}}{3}$
   

3. $2\pm \frac{4\sqrt{2}}{3}$
   

4. $1\pm \frac{4\sqrt{2}}{3}$

Q. If one end of the diameter is (1, 1) and other end lies on the line x + y = 3, then locus of centre of circle is

1. 2x + 2y = 5
2. x + y = 1
3. None of these
4. 2(x - y) = 5

Q. P is a point on the graph of $y=5x+3$. The coordinates of a point Q are $(3,-2)$. If $M$ is the mid-point of $PQ,$ then $M$ must lie on the line represented by

1. $y=5x-7$
2. $y=\frac{5}{2}x-\frac{7}{2}$
3. $y=\frac{5}{2}x+\frac{1}{2}$
4. $y=5x+1$

Q. How are the points $(0,1),(3,1)$ and $(1,3)$ situated with respect to the circle $x^2+y^2–2x–4y+3=0$

Q. How are the points $(-3,-1),(-2,3)$ and $(2,3)$ situated with respect to the circle $x^2+y^2+4x–2y+3=0$