$A$ circle touches the line $2x + y - 10 = 0$ at $(3, 4)$ and passes through the point $(1, -2)$. Then a point that lies on the circle is

$A$ parabola $y = ax^2 + bx + c$ crosses the $x$-axis at $(\alpha, 0)$ and $(\beta, 0)$,both to the right of the origin. $A$ circle also passes through these two points. The length of a tangent from the origin to the circle is:

Let $y^2 = 4ax$ be a parabola and $x^2 + y^2 + 2bx = 0$ be a circle. If the parabola and the circle touch each other externally,then:

From a point $P(0, b)$,two tangents are drawn to the circle $x^2+y^2=16$. These two tangents intersect the $X$-axis at two points $A$ and $B$. If the area of $\triangle PAB$ is minimum,then the equation of its circumcircle is

If a circle passes through the points of intersection of the coordinate axes with the lines $\lambda x - y + 1 = 0$ and $x - 2y + 3 = 0$,then the value of $\lambda$ is

For the two curves $C_1 : y^2 = 4x$ and $C_2 : x^2 + y^2 - 6x + 1 = 0$,which of the following is true?