Circle and a Point

If the point $\left(\lambda , 1+\lambda \right)$ lies inside the circle $x^2+y^2=1$, then

The equation of the radical axis of the circles $x^2+y^2+4x+6y-7=0$ and $4\left(x^2+y^2\right)+8x+12y-9=0$ is

If the points $\left(1,3\right)$ and $(2,k)$ are conjugated with respect the circle $x^2+y^2=35$, then the value of $k$ is

If the point $\left(1,4\right)$ lies inside the circle $x^2+y^2-6x-10y+p=0$ and the circle does not touch or intersect the coordinates axes, then

From the point $A\left(\mathrm{0,3}\right)$ on the circle $x^2+9x+{\left(y-3\right)}^2=0,$ a chord $AB$ is drawn and extended to a point $M$, such that $AM=2AB$ ( $B$ lies between $A$ & $M$). Then, the locus of the point $M$ is

The value of $a$ such that the power of the point $\left(1, 6\right)$ with respect to the circle $x^2+y^2+4x-6y-a=0$ is $-16$ is

The sum of the minimum and maximum distances of the point $(4, -3)$ to the circle $x^2+y^2+4x-10y-7=0$ is

The sum of the minimum and maximum distances of the point (4, -3) to the circle $x^2+y^2+4x-10y-7=0$ is

Difference between maximum & minimum distance of point $(2, -7)$ from $x^2+y^2-14x-10y-151=0$ is

Let $A(1, 2), B(3, 4)$ be two points and $C(x, y)$ be a point such that $(x – 1) (x – 3) + (y – 2) (y – 4) = 0$ . If area of $∆ABC$ is 1 sq. unit. Then maximum number of positions of C in $xy$ plane is

Maximum distance of any point on the circle  ${\left(\mathrm{x}\mathrm{ }-7\right)}^2+\mathrm{ }{\left(\mathrm{y}\mathrm{ }-2\mathrm{ }\sqrt{30}\right)}^2=16$ from the centre of the ellipse $25{\mathrm{x}}^2+\mathrm{ }16{\mathrm{y}}^2=400$ is

If the point $\left(2,k\right)$ lies outside the circles $x^2+y^2+x-2y-14=0 \& x^2+y^2=13$, then

$A\left(3,1\right),B\left(6,5\right)$ and $C\left(x,y\right)$ are three points such that angle $ACB$ is a right angle and the area of triangle $ABC=7\mathrm{sq}.\mathrm{unit}$ , then the number of such point $C$ is

The radius of the circle passing through the point $\left(6,2\right)$ and two of whose diameters are $x+y=6$ and $x+2y=4$ is -

If the point $\left(2, k\right)$ lies outside the circles $x^2+y^2=13$ and $x^2+y^2+x-2y-14=0,$ then

Difference between maximum & minimum distance of point $\left(2,\mathrm{ }–\mathrm{ }7\right)$ from ${\mathrm{x}}^2+{\mathrm{y}}^2–14\mathrm{x}–10\mathrm{y}–151=0$ is

Maximum distance of any point on the circle ${\left(\text{x}-7\right)}^2+{\left(\text{y}-2\sqrt{30}\right)}^2=16$ from the Centre of the ellipse 25x² + 16y² = 400 is

The range of $\alpha$, for which the point $\left(\alpha ,\alpha \right)$ lies inside the region bounded by the curves $y=\sqrt{1-x^2}$ and $x+y=1$, is:

The locus of centres of family of circle passing through the origin and cutting the circle $x^2+y^2+4x-6y-13=0$ orthogonally, is

The equation of circle is $x^2+y^2-2x=0$. The point $P(-1, 0)$ lies