If `x=asec thetacosphi,y=bsec thetasin phi and z=ctantheta,` show that, `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1`

If x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta , then prove that (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1.

If x=rcos thetacosphi,y=rcosthetasinphi and z=r sin theta, show that , x^2+y^2+z^2=r^2

If x=r cos theta cos phi, y=r cos theta sin phi, z=r sin theta , then prove that x^(2)+y^(2)+z^(2)=r^(2).

If x/a = y/b = z/c , then show that (x^(2)-yz)/(a^(2)-bc) = (y^(2)-zx)/(b^(2) - ca) = (z^(2)-xy)/(c^(2)-ab)

If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(theta+phi))=tanphi show that x^2/a^2+y^2/b^2=1

Let a ,b , c be the real numbers. The following system of equations in x ,y ,a n dz (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(c^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1 has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

If x = cy+bz, y =az+cx, z = bx+ay then prove that x^2/(1-a^2)=y^2/(1-b^2)=z^2/(1-c^2) .

If x,y,b and real, z=x+iy and (z-i)/(z-1)=ib, show that, (x-(1)/(2))^(2)+(y-(1)/(2))^(2)=(1)/(2).

If z = x + iy and |2z+1|=|z-2i| ,then show that 3(x^(2)+y^(2))+4(x+y)=3

If x : a = y : b = z : c,then show that : (a^2+b^2+c^2)(x^2+y^2+z^2) =(ax+by+cz)^2 .