" The pquation "(x^(2)-a^(2))^(2)(x^(2)-b^(2))+c^(4)(y^(2)-a^(2))^(2)=0" tepresents "(|a|!=|b|,c!=0)

if (x)/(a^(2)-b^(2))=(y)/(b^(2)-c^(2))=(z)/(c^(2)-a^(2)) , then prove that x+y+z=0.

The number of solution of the set of equations (x^(2))/a^(2)+(y^(2))/(b^(2))-(z^(2))/(c^(2))=0,(x^(2))/(a^(2))-(y^(2))/(b^(2))+(z^(2))/(c^(2))=0,-(x^(2))/(a^(2))+(y^(2))/(b^(2))+(z^(2))/(c^(2))=0 is

If H=(x^(2))/(a^(2))-(y^(2))/(b^(2))-1=0, C=(x^(2))/(a^(2))-(y^(2))/(b^(2))+1=0 and A=(x^(2))/(a^(2))-(y^(2))/(b^(2))=0 then H, A and C are in

If H=(x^(2))/(a^(2))-(y^(2))/(b^(2))-1=0, C=(x^(2))/(a^(2))-(y^(2))/(b^(2))+1=0 and A=(x^(2))/(a^(2))-(y^(2))/(b^(2))=0 then H, A and C are in

The value of x which satisfies the equation (x+a^(2)+2c^(2))/(b+c)+(x+b^(2)+2a^(2))/(c+a)+(x+c^2+2b^(2))/(a+b)=0 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

If H=(x^(2))/(a^(2))-(y^(2))/(b^(2))-1=0, C=(x^(2))/(a^(2))-(y^(2))/(b^(2))+1=0 and A=(x^(2))/(a^(2))-(y^(2))/(b^(2))=0 then H, A and C in

Area of quadrilateral formed by two pair of lines a^(2)x^(2)-b^(2)y^(2)-c(ax+by)=0 and a^(2)x^(2)-b^(2)y^(2)+c(ax-by)=0 is

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)