If the equation $x^{2}+y^{2}-10x+21=0$ has real roots $x=\alpha$ and $y=\beta,$ then

Let a circle passing through $(2,0)$ have its centre at the point $(h, k)$. Let $(x_c, y_c)$ be the point of intersection of the lines $3x + 5y = 1$ and $(2+c)x + 5c^2y = 1$. If $h = \lim_{c \to 1} x_c$ and $k = \lim_{c \to 1} y_c$,then the equation of the circle is:

The equation of the circle passing through the origin,whose center lies in the first quadrant and which makes intercepts of length $6$ and $4$ on the $x$-axis and $y$-axis respectively,is:

Which of the following is the equation of a circle?

If the parametric equations of the circle passing through the points $(3,4)$,$(3,2)$,and $(1,4)$ are $x=a+r \cos \theta$ and $y=b+r \sin \theta$,then find the value of $b^{a} r^{a}$.

The abscissae of two points $P$ and $Q$ are the roots of the equation $2x^2 + 4x - 7 = 0$ and their ordinates are the roots of the equation $3x^2 - 12x - 1 = 0$. Then the centre of the circle with $PQ$ as a diameter is