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 (a) `(x^2+y^2)^2+a^2(x^2-y^2)=4a^2` (b)`2(x^2+y^2)^2+4a^2(x^2-y^(2))=4a^2` (c)`(x^2+y^2)^2+4a^2(x^2-y^2)=4a^2` (d)`(x^2+y^2)+a^2(x^2-y^(2))=a^4`

Locus of all such points from where the tangents drawn to the ellipse x^2/a^2 + y^2/b^2 = 1 are always inclined at 45^0 is: (A) (x^2 + y^2 - a^2 - b^2)^2 = (b^2 x^2 + a^2 y^2 - 1) (B) (x^2 + y^2 - a^2 - b^2)^2 = 4(b^2 x^2 + a^2 y^2 - 1) (C) (x^2 + y^2 - a^2 - b^2)^2 = 4(a^2 x^2 + b^2 y^2 - 1) (D) none of these

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^2y^2dot

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

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=4x y (b) (x^2-y^2)=1/9 (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 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 x y=1 on a variable tangent is (x^2+y^2)^2=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

Add : x^(2) y^(2) , 2x^(2)y^(2) , - 4x^(2)y^(2) , 6x^(2)y^(2)

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 (A) (x^2+y^2)(1/(x^2)+1/(y^2))=4a^2 (B) (x^2+y^2)^2(1/(x^2)+1/(y^2))=a^2 (C) (x^2+y^2)^2(1/(x^2)+1/(y^2))=4a^2 (D) (x^2+y^2)(1/(x^2)+1/(y^2))=a^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

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