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

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. -20

2. 0

3. 5

4. Cannot be determined

Q.

The equation of the straight line whose perpendicular distance from origin is $3\sqrt{2}$ units and this perpendicular makes an angle of ${75}^{\circ }$ with the positive direction of x-axis, is

1. 

2. 

3. 

4. 

Q. If $g^2+f^2=c,$ then the equation $x^2+y^2+2gx+2fy+c=0$ will represent

1. A circle of radius g

2. A circle of radius f

3. A circle of diameter $\sqrt{c}$

4. A circle of radius 0

Q. The centre and radius of the circle $2x^2+2y^2-x=0$ are

1. $(\frac{1}{4},0)and\frac{1}{4}$
2. $(-\frac{1}{2},0)and\frac{1}{2}$
3. $(\frac{1}{2},0)and\frac{1}{2}$
4. $(0,-\frac{1}{4})and\frac{1}{4}$

Q. The equation $x^2+y^2+4x+6y+13=0$ represents

1. Circle

2. Pair of coincident straight lines

3. Pair of concurrent straight lines

4. Point

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

1. A circle

2. x-axis
3. y-axis

4. A point

Q. Radius of the circle $x^2+y^2+2xcos\theta +2ysin\theta -8=0,$ is

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

Q. Find the shortest distance between the curve $y^2=x^3$ and $9x^2+9y^2-30y+16=0$.?

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

1. $\sqrt{13}$
2. $\sqrt{10}$
3. $\sqrt{2}$
4. $\sqrt{24}$

Q. Question 12
The points A(-1, -2), B(4, 3), C(2, 5) and D(-3, 0) in that order form a rectangle.

Q. If the radius of the circle $x^2+y^2-18x+12y+k=0$ be 11, then k =

1. 347
2. 4
3. -4
4. 49

Q. If radii of two concentric circles are $4$ cm and $5$ cm, then the length of each chord of one circle which is tangent to the circle is

1. $6$ cm
2. $3$ cm
3. $9$cm
4. $1$ cm

Q. The area of the curve $x^2+y^2=2ax$ is

1. $\pi a^2$
2. $2\pi a^2$
3. $4\pi a^2$
4. $\frac{1}{2}\pi a^2$

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. Find the centre and radius of the circle $x^2+y^2-4x-6y+11=0$