Obtaining Centre and Radius of a Circle from General Equation of a Circle

Q. The equation $x^2+y^2=0$ denotes

1. A point

2. A circle

3. x-axis
4. y-axis

Q. If the line x + 2by + 7 = 0 is diameter of the circle $x^2+y^2-6x+2y=0$, then b =

1. 3
2. -5
3. -1
4. 5

Q. Centre of the circle $(x-3{)}^2+(y-4{)}^2$ = 5 is

1. (3, 4)
2. (-3, -4)
3. (4, 3)
4. (-4, -3)

Q. If one of the diameters of the circle, given by the equation $x^2+y^2-4x+6y-12=0$, is a chord of a circle S, whose centre is at (-3, 2), then the radius of S is

1. $5\sqrt{2}$
2. $5\sqrt{3}$
3. $5$
4. $10$

Q.

An infinite number of tangents can be drawn from (1, 2) to the circle $x^2+y^2-2x-4y+\lambda =0,$ then $\lambda =$

1. 5

2. Cannot be determined

3. -20

4. 0

Q.

The number of integral values of $\lambda$ for which $x^2+y^2+\lambda x+(1-\lambda )y+5=0$ is the equation of a circle whose radius cannot exceed 5, is

1. 14

2. 16
   

3. 18
   

4. none of these

Q. The number of integral values of $\lambda$ for which $x^2+y^2+\lambda x+(1-\lambda )y+5=0$ is the equation of a circle whose radius cannot exceed $5$, is:

1. $14$
2. $18$
3. $16$
4. None

Q. If $y=2x+K$ is a diameter to the circle $2(x^2+y^2)+3x+4y-1=0$, then $K$ equals

1. $1$
2. $2$
3. $\frac{1}{2}$
4. $0$

Q. Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the distance between origin and the point of intersection of other line with the cordinate axes.

1. $7$
2. $3$
3. $4$
4. $5$

Q. The radius of the circle $x^2+y^2+4x+6y+13=0$ is

1. $\sqrt{26}$
2. $\sqrt{13}$
3. $\sqrt{23}$
4. 0

Q. In a triangle with sides a, b, and c, a semicircle touching the sides AC and CB is inscribed whose diameter lies on AB. Then, the radius of the semicircle is

1. a/2
2. $\Delta /s$
3. $\frac{2\Delta }{a+b}$
4. $\frac{2abc}{\left(s\right)(a+b)}cos\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}$