Show the condition that the curves `a x^2+b y^2=1` and `a^(prime)\ x^2+b^(prime)\ y^2=1` Should intersect orthogonally

Show the condition that the curves a x^2+b y^2=1 and Ax^2+By^2=1 should intersect orthogonally is 1/a-1/b=1/A-1/Bdot

Find the condition for the two concentric ellipses a_1x^2+\ b_1y^2=1\ a n d\ a_2x^2+\ b_2y^2=1 to intersect orthogonally.

Show that x^2+4y^2=8 and x^2-2y^2=4 intersect orthogonally

If two curves ax^2 +by^2=1 and a'x^2+b'y^2=1 intersect orthogonally,then show that 1/a-1/b=1/[a']-1/[b']

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

Show that x^3-3x y^2=(-2) and 3x^2\ y-y^3=2 intersect orthogonally.

Show that y=x^3 and 6y=7-x^2 intersect orthogonally:

If the curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect orthogonally, then

If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2y^2+2a x+2b y+c=0 intersect othrogonally, then prove that a a^(prime) + b b prime=c+c^(prime)/2dot

If the abscissae and the ordinates of two point Aa n dB be the roots of a x^2+b x+c=0a n da^(prime)y^2+b^(prime)y=c^(prime)=0 respectively, show that the equation of the circle described on A B as diameter is a a^(prime)(x^2+y^2)+a^(prime)b x+a b^(prime)y+(c a^(prime)+ca)=0.