The locus of the foot of the perpendicular from the centre of the hyperbola `xy = c^2` on a variable tangent is (A) `(x^2-y^2)=4c^2xy` (B) `(x^2+y^2)^2=2c^2xy` (C) `(x^2+y^2)=4c^2xy` (D) `(x^2+y^2)^2=4c^2xy`

The locus of the foot of the perpendicular from the centre of the hyperbola xy=c^(2) on a variable tangent is (A) (x^(2)-y^(2))=4c^(2)xy(B)(x^(2)+y^(2))^(2)=2c^(2)xy(C)(x^(2)+y^(2))=4c^(2)xy(D)(x^(2)+y^(2))^(2)=4c^(2)xy

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (a) (x^(2)+y^(2))^(2)=4xy (b) (x^2-y^2)=1/9 (c) (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

The locus of the foot of the perpendicular from the center of the hyperbola xy=1 on a variable tangent is (x^(2)-y^(2))=4xy(b)(x^(2)-y^(2))=(1)/(9)(x^(2)-y^(2))=(7)/(144)(d)(x^(2)-y^(2))=(1)/(16)

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

Simplify : (x^(2) - y^(2) + 2xy + 1) - (x^(2) + y^(2) + 4xy - 5)

Prove that the locus of the mid-points of chords of length 2d unit of the hyperbola xy=c^(2) is (x^(2)+y^(2))(xy-c^(2))=d^(2)xy.

Prove that the locus of the mid-points of chords of length 2d units of the hyperbola xy=c^2 is (x^2+y^2)(xy-c^2)=d^2xy

The parabola y^(2)=4x cuts orthogonally the rectangular hyperbola xy=c^(2) then c^(2)=

A variable straight line of slope 4 intersects the hyperbola xy=1 at two points. Then the locus of the point which divides the line segment between these two points in the ratio 1:2 , is (A) x^2 + 16y^2 + 10xy+2=0 (B) x^2 + 16y^2 + 2xy-10=0 (C) x^2 + 16y^2 - 8xy + 19 = 0 (D) 16x^2 + y^2 + 10xy-2=0