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1.
Equation of normal to the parabola 
which passes through 
is
which passes through is
2.
Let 
be the centre of the ellipse 
If the tangent at any point on the ellipse cuts the coordinate axes in 
and 
respectively, then 
be the centre of the ellipse If the tangent at any point on the ellipse cuts the coordinate axes in and respectively, then
3.
The equation of the circle having 
and 
as two tangents and 
as a diameter is
and as two tangents and as a diameter is
4.
If 
lies on the circle 
which is concentric with the circle 
, then 
is equal to
lies on the circle which is concentric with the circle , then is equal to
5.
The equation of the circumcircle of the triangle formed by the lines 
is
is
6.
Circles are drawn through the point 
to cut intercepts of length 5 units on the 
-axis. If their centres lie in the first quadrant, then their equation is
to cut intercepts of length 5 units on the -axis. If their centres lie in the first quadrant, then their equation is
7.
The number of points with integral coordinates with lie in the interior of the region common to the circle 
and the parabola is
and the parabola is
8.
If the chords of contact of the tangents from a point on the circle 
to the circle 
touch the circle 
then the roots of the equation 
, are
to the circle touch the circle then the roots of the equation , are
9.
If the vertex and focus of a parabola are 
and 
respectively, then its equation is
and respectively, then its equation is
10.
If the length of the major axis of an ellipse is three times the length of its minor axis, its eccentricity, is