" 5.Show that the set of curves intersect orthogonally: "x^(2)+4y^(2)=8" and "x^(2)-2y^(2)=4" ."

Show that the following curves cut each other orthogonally: x^2 + 4y^2 =8 and x^2-2y^2=4

Show that the following set of curves intersect orthogonally: y=x^(3) and 6y=7-x^(2)x^(3)-3xy^(2)=-2 and 3x^(2)y-y=2x^(2)+4y^(2)=8 and x^(2)-2y^(2)=4

Show that the following set of curves intersect orthogonally: (i) y=x^3 and 6y=7-x^2 , (ii) x^3-3x y^2=-2 and 3x^2y-y^3=2. (iii) x^2+4y^2=8 and x^2-2y^2=4

Show that the following curves cut orthogonally 4y^(2)-x^(2)=8, 2x^(2)+y^(2)=20

Find the condition for the following set of curves to intersect orthogonally: (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(A^2)-(y^2)/(B^2)=1.

Find the condition for the following set of curves to intersect orthogonally: (x^2)/(a^2)-(y^2)/(b^2)=1 and x y=c^2 (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(A^2)-(y^2)/(B^2)=1.

Prove that the curve y=x^(2) and xy=k intersect orthogonally if 8k^(2)=1

Show that x^2=4y and 4y+x^2=8 intersect orthogonally at (2,\ 1)

Show that x^2=4y and 4y+x^2=8 intersect orthogonally at (2,\ 1)

Prove that the curve y = x^2 and xy = k intersect orthogonally if 8k^2 = 1 .