The locus of a point, from where the tangents to the rectangular hyperbola `x^2-y^2=a^2` contain an angle of `45^0` , is `(x^2+y^2)^2+a^2(x^2-y^2)=4a^2` `2(x^2+y^2)^2+4a^2(x^2-y^(2))=4a^2` `(x^2+y^2)^2+4a^2(x^2-y^2)=4a^2` `(x^2+y^2)+a^2(x^2-y^(2))=a^4`

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is (x^2+y^2)(1/(x^2)+1/(y^2))=4a^2 (x^2+y^2)^2(1/(x^2)+1/(y^2))=a^2 (x^2+y^2)^2(1/(x^2)+1/(y^2))=4a^2 (x^2+y^2)(1/(x^2)+1/(y^2))=a^2

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^(2)-y^(2)=a^(2) is a^(2)(y^(2)-x^(2))=4x^(2)y^(2)

The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+""3y^2=""6 on any tangent to it is (1) (x^2-y^2)^2=""6x^2+""2y^2 (2) (x^2-y^2)^2=""6x^2-2y^2 (3) (x^2+y^2)^2=""6x^2+""2y^2 (4) (x^2+y^2)^2=""6x^2-2y^2

Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circle x^(2)+y^(2)=1

The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy=c^(2) is (A)(x^(2)-y^(2))^(2)+4c^(2)xy=0(B)(x^(2)+y^(2))^(2)+4c2^(x)y=0(C)x^(2)-y^(2))^(2)+4c2^(x)y=0(C)x^(2)-y^(2))^(2)+4cxy=0(D)(x^(2)+y^(2))^(2)+4cxy=0

The locus of the midde points ofchords of hyperbola 3x^(2)-2y^(2)+4x-6y=0 parallel to y=2x is

Circles x^(2)+y^(2)=4 and x^(2)+y^(2)-2x-4y+3=0