Circles — Class 12 Mathematics PYQs

If $(a,b)$ is the centre and $c$ is the radius of the circle $x^2+y^2+2x+6y+1=0$, then what is the value of $a^2+b^2+c^2$?

Direction : Consider the following for the two (02) items that follow :

A triangle $ABC$ is inscribed in the circle $x^2+y^2=100$. $B$ and $C$ have coordinates $(6,8)$ and $(-8,6)$ respectively.

What are the coordinates of $A$?

If $3x+y-5=0$ is the equation of a chord of the circle $x^2+y^2-25=0$, then what are the coordinates of the mid-point of the chord ?

Consider the following in respect of the circle $4x^2+4y^2-4ax-4ay+a^2=0$ :

1. The circle touches both the axes.
2. The diameter of the circle is $2a$.
3. The centre of the circle lies on the line $x+y=a$.

How many of the statements given above are correct ?

What is the equation of the circle which touches both the axes in the first quadrant and the line $y-2=0$ ?

Direction : Consider the following for the next two (02) items that follow.

A circle is passing through the points $(5,-8)$, $(-2,9)$ and $(2,1)$.

What are the coordinates of the centre of the circle?

Direction : Consider the following for the next two (02) items that follow.

A circle is passing through the points $(5,-8)$, $(-2,9)$ and $(2,1)$.

If $r$ is the radius of the circle, then which one of the following is correct?

What is the radius of the circle $4x^2+4y^2-20x+12y-15=0$?