EXERCISE 12.4

Locus of centres of the circles which touch the two circles $x^2+y^2=16$ and $x^2+y^2=16x$ externally is

The locus of the centre of the circles which cut the circles $x^2+y^2+4x-6y+9=0$ and  $x^2+y^2-4x+6y+4=0$ orthogonally is

Locus of the foot of perpendicular drawn from a fixed point $(10, 0)$ on the $x$-axis to any tangent to the circle $x^2+y^2=16$ is

The tangent at any point on circle $x^2+y^2=(\sqrt{2}{)}^2$ cuts the axes in $L$ and $M,$ then locus of midpoint of $LM$ is

A triangle has two of its sides along the axes, its third side touches the circle $x^2+y^2-4x-4y+4=0$ locus of circumcentre of triangle is

The point$A\left(2,4\right)$ is joined to any point $P$ of the circle $x^2+y^2=4$.The locus of midpoint of $AP$ as $P$ moves on circle is

Four distinct points $\left(0,0\right), \left(0,1\right), \left(1,0\right), \left(2k,3k\right)$ lie on a circle. Then the value of $k$ is

The circle $x^2+y^2-6x-10y+k=0$ does not touch or intersect the $x$-axis and the point $(1,4)$ lies inside the circle, then