`ax^2+by^2=1" and "Ax^2+By^2=1` meet each other orthogonally. `(aneA,bneB,aB-bA ne0)`. Show that `(1)/(a)-(1)/(b)=(1)/(A)-(1)/(B)`.

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)

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

If the circles x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other, prove that, (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

If sin A+ tan A= a and cos A+ cot A= b, then show that (1+a)^(-2)+(1+b)^(-2)=(1-ab)^(-2)

If the roots of the equation ax^2+bx+c=0 are alpha and beta then show that 1/(a alpha+b)+1/(abeta+b)=b/(ac) .

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then, (a) a_(1)/a_(2)=b_(1)/b_(2) (b) a_(1)a_(2)=b_(1)b_(2) (c) a_(1)a_(2)+b_(1)b_(2)=0 (d) a_(1)-a_(2)=b_(1)-b_(2)

If a^2/(b+c)=b^2/(c+a)=c^2/(a+b)=1 , show that 1/(1+a)+1/(1+b)+1/(1+c)=1

If a+b+c= 0 prove that 1/(2a^2+bc)+1/(2b^2+ca)+1/(2c^2+ab)=0

If a^(2)+b^(2)=7ab show that log[1/3(a+b)]=1/2(log a+logb)