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1.
The circle 
cuts an intercept on 
-axis of length
cuts an intercept on -axis of length
2.
If the eccentricities of the ellipse 
and the hyperbola 
are reciprocals of each other, then 
is equal to
and the hyperbola are reciprocals of each other, then is equal to
3.
The ellipse 
is inscribed in a rectangle aligned with the coordinate axes, which is turn in inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is
is inscribed in a rectangle aligned with the coordinate axes, which is turn in inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is
4.
The Cartesian equation of the directrix of the parabola whose parametric equations are 
is
is
5.
The line 
is the directrix of the parabola 
Then one of the value of 
is
is the directrix of the parabola Then one of the value of is
6.
The equation of the axes of the ellipse 
are
are
7.
Locus of the mid points of the chord of ellipse 
, so that chord is always touching the circle 
, 
is
, so that chord is always touching the circle , is
8.
The length intercepted by the curve 
on the line satisfying 
and passing through point (0, 1), is given by
on the line satisfying and passing through point (0, 1), is given by
9.
Two vertices of an equilateral triangle are 
and 
and its third vertex lies above the x-axis. The equation of its circumcircle, is
and and its third vertex lies above the x-axis. The equation of its circumcircle, is
10.
The tangents to 
having inclinations 
and 
intersect at 
If 
then the locus of P is
having inclinations and intersect at If then the locus of P is