Let r be a positive constant. If two curves `C_1: y = (2x^2)/(x^2+1)" and "C_2: y=sqrt(r^2-x^2)` intersects orthogonally then r cannot be

Let r be a positive constant.If two curves C_(1):y=(2x^(2))/(x^(2)+1) and C_(2):y=sqrt(r^(2)-x^(2)) intersect orthogonally then r cannot be

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

If the curve ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 intersect orthogonally, then

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

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

Prove that the curve 2x^(2)+3y^(2)=1 and x^(2)-y^(2)=(1)/(12) intersect orthogonally.

If curve x^(2)=9a(9-y) and x^(2)=a(y+1) intersect orthogonally then value of 'a' is

If curve x^2=9a(9-y) and x^2=a(y+1) intersect orthogonally then value of 'a' is

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

Let 'a' be a positive constant number. Consider two curves C_1: y=e^x, C_2:y=e^(a-x) . Let S be the area of the part surrounding by C_1, C_2 and the y axis, then Lim_(a->0) s/a^2 equals