If the curves `ax^2 + by^2 =1 and a'x^2 +b'y^2 =1` intersect orthogonally, prove that: `1/a-1/a'=1/b-1/b'`

If the curves: alphax^2 + betay^2 =1 and alpha'x^2 + beta'y^2=1 intersect orthogonally, prove that (alpha-alpha') betabeta' = (beta-beta') alphaalpha'

If curve y = 1 - ax^2 and y = x^2 intersect orthogonally then the value of a is

If ax^(2)+by^(2)=1 cut a'x^(2)+b'y^(2)=1 orthogonally, then

Find the condition for the curves: x^2/a^2-y^2/b^2=1,xy=c^2 to intersect orthogonally.

Find the condition for the curves (X^2)/(a^2) - (y^2)/(b^2) = 1 and xy = c^2 to intersect orthogonally.

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a,b,c and a',b',c' respectively form the origin, prove that 1/a^2+1/b^2+1/c^2=1/(a'^2)+1/(b'^2)+1/(c'^2) .

Show that the curves y = a^x and y = b^x , a gt b gt 0 intersect at an angle of tan^-1 (|(log(a/b)/(1+log a logb))|)

The slope of the curve 2y^2=a x^2+ba (1,-1) is -1 Find a , b

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

Ax^2+By^2=1 , A and B are arbitrary constants.