If the curves `(x^(2))/(a)+(y^(2))/(b)=1 and (x^(2))/(c )+(y^(2))/(d)=1` intersect at right angles then prove that `a-b=c-d`

If the curves ax^(2)+by^(2)=1 and cx^(2)+dy^(2)=1 intersect at right angles then show that (1)/(a)-(1)/(b)=(1)/(c)=(1)/(d)

Show that curves x^(3)-3xy^(2)+2=0 and y^(3)-3x^(2)y+2=0 intersect at right angles.

If c=a+b, then show that the curves x^((2)/(3))+y^((2)/(3))=c^((2)/(3)) and (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touch each other.

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

The curves x^2/a+y^2/b=1 and x^2/a_1+y^2/b_1=1 will cut orthogonally if (a-b) =

Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if , 1/a-1/b=1/c-1/d

The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at right angles. Then the equation of the circle through the points of intersection of two conics is (a) x^2+y^2=5 (b) sqrt(5)(x^2+y^2)-3x-4y=0 (c) sqrt(5)(x^2+y^2)+3x+4y=0 (d) x^2+y^2=25

If (x/a)+(y/b)=1 and (x/c)+(y/d)=1 intersect the axes at four concylic points and a^2+c^2=b^2+d^2, then these lines can intersect at, (a , b , c , d >0)

The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0 at the origin intersect at an angle theta equal to (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1 and to cut the ellipse x^2/c^2+y^2/d^2=1 at the points P and Q. If the tangents are at right angles, then the value of (a^2/c^2)+(b^2/d^2) is