General Equation of a Circle

Q.

Find the equation of the circle which passes through the centre of the circle $x^2+y^2+8x+10y-7=0$ and is concentric with the circle $2x^2+2y^2-8x-12y-9=0.$

Q.

Find the cente and radius of the following circle.
$x^2+y^2-8x-10y-12=0$

Q.

The equation of a circle which passes through (1, 2) and (2, 1) and whose radius is 1 units is

1. x ²+y²-4x-4y+7=0

2. x ²+y²-2x-4y+4=0

3. x ²+y²-4x-2x+4=0

4. x ²+y²-x-y+1=0

Q. The equation of the circle passing through the point (1, –2) and having its centre on the line 2x – y – 14 = 0 and touching the line 4x + 3y – 23 = 0

1. + - 8x + 12y + 27 = 0
2. + + 8x + 12y + 27 = 0
3. + - 12y + 27 = 0
4. + - 8x + 12y + 27 = 0

Q.

Which of the following equations represents a circle with centre $(g,f)$ and radius $\sqrt{g^2+f^2+c}$ ?

1. $x^2+y^2+2gx+2fy+c=0$

2. $x^2+y^2-2gx-2fy+c=0$

3. $x^2+y^2+2gx+2fy-c=0$

4. $x^2+y^2-2gx-2fy-c=0$

Q.

The centre and radius of the circle $x^2+y^2+2gx+2yf+c=0$ are and respectively.

1. $\sqrt{g^2+f^2-c}$
2. $\sqrt{g^2+f^2+c}$
3. $(-g,-f)$
4. $(g,f)$

Q.

The equation of circle concentric with circle $x^2+y^2-6x+12y+15$ = 0 and double its area is

1. x ²+y²-6x+12y-15=0

2. x ²+y²-6x+12y+20=0

3. x ²+y²-6x+12y+45=0

4. x ²+y²-6x+12y-30=0

Q.

Find centre and radius for the given equation of the circle.

$x^2+y^2-4x-8y-45=0$

Q.

Which of the following gives the equation of director circle of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$?

1. x² - y² = 9

2. x² + y² = 41

3. x² + y² = 9

4. x² + y² = 25

Q. The radius of the circle, $x^2+y^2-2x+4y-11=0$ is .

1. 1
2. 2
3. 3
4. 4

Q.

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

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Q.

Find the equation of director circle of a circle whose equation is $x^2+y^2-4x+6y+12=0$

1. 

2. 

3. 

4. 

Q.

Find the equation of circle, if the lines $2x-3y=5$and $3x-4y=7$are diameters of a circle of area 154 sq units.

Q.

How do you find the equation of a circle with center at the origin and passing through $\left(-6,-2\right)$?

Q. Find the equation of the circle with centre $(-a,-b)$ and radius $\sqrt{a^2-b^2}$

Q. The centres of the circles $x^2+y^2=1,$ $x^2+y^2+6x-2y=1$ and $x^2+y^2-12x+4y=1$ are

1. Collinear
2. same
3. Non–collinear
4. None of these

Q.

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{16}=1$ and having the centre at (0, 3) is

(IIT JEE Main 2013)

1. $x^2+y^2-6y-7=0$

2. $x^2+y^2-6y+7=0$

3. $x^2+y^2-6y+5=0$

4. $x^2+y^2-6y-5=0$

Q. Find the centre and radius of the circle $(x+5){}^2+(y-3){}^2=36$

Q.

If $(h,k)$ is the centre of $x^2+y^2-2x-4y+11=0$, find the value of $h^2+k^2+hk$.

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Q.

Find the cente and radius for the following circle.
$2x^2+2y^2-x=0$

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