Equation of the Circle Using End Points of Diameter

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. Compare the given equation of the circle and then find the value of $a+b+c+d+e$ if the centre of the circle is at origin (2, 0) and radius is 6.
given equation : $a{x}^2+b{y}^2+cx+dy+e=0$

Q.

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

___

Q.

Consider the points $A(3,2),B(9,4),C(7,10)$. Then the circle with AC as diameter doesn't pass through B.

1. False

2. True

Q.

The equation of the circle having $(3,3)$ and origin as the endpoints of its diameter is

1. $x^2+y^2-3(x+y)=0$

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

3. $(x+y{)}^2-2xy-3(x+y)=0$

4. $(x+y{)}^2+2xy-3x+y=0$

Q.

The equation of the circle having $(4,-1)$ and $(2,-1)$ as the endpoints of its diameter is

1. $x^2+y^2-x+2y+9=0$

2. $x^2+y^2-6x+2y-9=0$

3. $x^2+y^2+x+y-9=0$

4. $x^2+y^2-6x+2y+9=0$

Q.

The equation of the circle having $(-2,-1)$ and $(2,1)$ as the endpoints of its diameter is

1. $x^2+y^2=5$

2. $x^2-y^2=5$

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

4. $x^2-y^2=-5$

Q.

Equation of the circle passing through $(2,3)$ and centre at the origin is _______ .

1. $(x-2{)}^2+(y-3{)}^2=13$

2. $x^2+y^2=13$

3. $(x-3{)}^2+(y-2{)}^2=13$

4. $x^2-y^2=13$

Q.

The equation of the circle having $(6,7)$ and $(4,3)$ as the endpoints of its diameter is

1. $(x+y{)}^2-2xy+45=0$

2. $(x^2-y^2-2xy+45=0$

3. $10(x+y)-2xy+45=0$

4. $(x+y)\left[\right(x+y)-10]-2xy+45=0$

Q.

The equation of the circle having $(-2,1)$ and $(4,-1)$ as the endpoints of its diameter is

1. $x^2+y^2-2x-9=0$

2. $x^2+y^2-2x+9=0$

3. $x^2+y^2+2x+9=0$

4. $x^2+y^2+2x-9=0$