Circles — NDA Mathematics PYQs

Directions : For the next two (02) items that follow :
Consider the points $A(0,2)$, $B(2,3)$, $C(4,5)$ and $D(0,k)$.

If the points lie on a circle, then what is/are the possible value(s) of k ?

Directions : For the next two (02) items that follow :
Consider the points $A(0,2)$, $B(2,3)$, $C(4,5)$ and $D(0,k)$.

If a circle is drawn through A, B and D, then what is the diameter of the circle ?

What is the equation of the circle whose diameter is $10$ cm and the equations of two of its diameters are $x+y=0$ and $x-y=0$?

A square is inscribed in a circle $x^2+y^2+2x+2y+1=0$ and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?

The circle $x^2+y^2-2kx-2ky+k^2=0$ touches the $x$-axis at $P$ and $y$-axis at $Q$. What is $PQ$ equal to?

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 $a^2+b^2+c^2$ ?

The equation of a circle is $(x^2-4x+3)+(y^2-6y+8)=0$. Which of the following statements are correct?

I. The end points of a diameter of the circle are at $(1,2)$ and $(3,4)$.
II. The end points of a diameter of the circle are at $(1,4)$ and $(3,2)$.
III. The end points of a diameter of the circle are at $(2,4)$ and $(4,2)$.

Select the answer using the code given below.

Directions : 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 is $\angle BAC$ equal to?

Directions : 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 $A$?

*Directions : Consider the following for the next two (02) items that follow :

The line $y=x$ partitions the circle $(x-a{)}^2+y^2=a^2$ in two segments.*

What is the area of minor segment ?