Find the values of `a` for which three distinct chords drawn from `(a ,0)` to the ellipse `x^2+2y^2=1` are bisected by the parabola `y^2=4xdot`

Find the equations of the tangents drawn from the point (2, 3) to the ellipse 9x^2+16 y^2=144.

Find the number of distinct normals that can be drawn from (-2,1) to the parabola y^2-4x-2y-3=0

Find the point where the line x+y=6 is a normal to the parabola y^2=8xdot

Find the condition on aa n db for which two distinct chords of the hyperbola (x^2)/(2a^2)-(y^2)/(2b^2)=1 passing through (a , b) are bisected by the line x+y=b .

Find the range of values of m for which the line y=m x+2 cuts the circle x^2+y^2=1 at distinct or coincident points.

If two distinct chords, drawn from the point (p, q) on the circle x^2+y^2=p x+q y (where p q!=q) are bisected by the x-axis, then (a) p^2=q^2 (b) p^2=8q^2 (c) p^2 8q^2

Find the locus of the midpoint of normal chord of parabola y^2=4ax

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.

Find the angle between the tangents drawn from (1, 3) to the parabola y^2=4xdot

Find the locus of the middle points of all chords of (x^2)/4+(y^2)/9=1 which are at a distance of 2 units from the vertex of parabola y^2=-8a xdot