### Mathematics - Circle

#### Question - 1

Length of the diameter of circle ${ X }^{ 2 }+{ Y }^{ 2 }-8X+6Y-5=0$ is

• A $4\sqrt{30}$
• B $2\sqrt{30}$
• C $3\sqrt{30}$
• D 30

#### Question - 2

Find the equation of circle having centre $\left( \frac { 1 }{ 2 } ,\frac { 1 }{ 4 } \right)$ and radius $\frac{1}{12}$

• A $36{ x }^{ 2 }+36{ y }^{ 2 }-36x-18y-11=0$
• B $36{ x }^{ 2 }+36{ y }^{ 2 }+36x+18y+11=0$
• C $36{ x }^{ 2 }+36{ y }^{ 2 }-36x-18y+11=0$
• D None of the above

#### Question - 3

Equation of the diameter of the circle ${ x }^{ 2 }+{ y }^{ 2 }-12x+4y+6=0$ is given by

• A x + y = 0
• B x + 3y = 0
• C x = y
• D 3x + 2y = 0

#### Question - 4

Equation of the circle with centre on the Y-axis and passing through the origin and the point (2, 3) is

• A ${ x }^{ 2 }+{ y }^{ 2 }+13y=0$
• B ${ 3x }^{ 2 }+{ 3y }^{ 2 }+13x+3=0$
• C ${ 6x }^{ 2 }+{ 6y }^{ 2 }-26y=0$
• D ${ x }^{ 2 }+{ y }^{ 2 }+13x+3=0$

#### Question - 5

The equation of the circle which passes through the origin and makes intercept of lengths a and b on the X and Y-axes respectively, are

• A ${ x }^{ 2 }+{ y }^{ 2 }\pm ax\pm by=0$
• B ${ x }^{ 2 }\pm { y }^{ 2 }=0$
• C ${ x }^{ 2 }\pm ax\pm by=0$
• D None of the above

#### Question - 6

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line Y - 4X + 3 = 0.

• A ${ x }^{ 2 }+{ y }^{ 2 }-4x-10y+25=0$
• B ${ x }^{ 2 }+{ y }^{ 2 }-4x-10y-25=0$
• C ${ x }^{ 2 }+{ y }^{ 2 }-4x+10y-25=0$
• D None of the above

#### Question - 7

Find the equation of a circle which touches both the axes and the line 3X - 4Y + 8 = 0 and lies in the third quadrant.

• A ${ x }^{ 2 }+{ y }^{ 2 }+4x+4y-4=0$
• B ${ x }^{ 2 }+{ y }^{ 2 }-4x-4y+4=0$
• C ${ x }^{ 2 }+{ y }^{ 2 }+4x+4y+4=0$
• D None of the above

#### Question - 8

${ X }^{ 2 }+{ Y }^{ 2 }+4X-6Y+4=0$ is the equation of the incircle of an equilateral triangle, then the equation of the circumcircle of the triangle is

• A ${ x }^{ 2 }+{ y }^{ 2 }+4x+6y-23=0$
• B ${ x }^{ 2 }+{ y }^{ 2 }+4x-6y-23=0$
• C ${ x }^{ 2 }+{ y }^{ 2 }-4x-6y-23=0$
• D None of the above

#### Question - 9

The circle ${ X }^{ 2 }+{ Y }^{ 2 }-2X+4Y+3=0$ has a square inscribed in it. Sides of the square are parallel to the coordinate axes. Then, one vertex of the square is

• A $\left( 1+\sqrt { 2 } ,-2 \right)$
• B $\left( 1-\sqrt { 2 } ,-2 \right)$
• C $\left( 1,-2+\sqrt { 2 } \right)$
• D None of the above

#### Question - 10

The circle ${ x }^{ 2 }+{ y }^{ 2 }={ r }^{ 2 }$ intersects the line Y = mX + c at the two real distinct points, if

• A $-r\sqrt { 1+{ m }^{ 2 } }$
• B $-c\sqrt { 1-{ m }^{ 2 } }$
• C $-r\sqrt { 1-{ m }^{ 2 } }$
• D None of the above