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1.
The equation of a circle which cuts the three circles
orthogonally, is
orthogonally, is
2.
The length of the common chord of the ellipse 
and the circle 
is
and the circle is
3.
The mirror image of the directrix of the parabola 
in the line mirror 
is
in the line mirror is
4.
The line 
meets the ellipse 
in the real points, if
meets the ellipse in the real points, if
5.
The length of the latusrectum of the hyperbola 
is
is
6.
The condition that the chord 
of 
may subtend a right angle at the centre of the circle is
of may subtend a right angle at the centre of the circle is
7.
Given that circle 
and 
touch, the equation to their common tangent is
and touch, the equation to their common tangent is
8.
The number of common tangents of the circles 
and 
is
and is
9.
A ray of light incident at the point 
gets reflected from the tangent at 
to the circle 
The reflected ray touches the circle. The equation of the line along which the incident ray moved is
gets reflected from the tangent at to the circle The reflected ray touches the circle. The equation of the line along which the incident ray moved is
10.
If the points 
and 
are symmetrical about the tangent to the circle 
at the origin, then the coordinates of are
and are symmetrical about the tangent to the circle at the origin, then the coordinates of are