[(sqrt(10)))/(a)+(y)/(b)=a+b],[(x)/(a^(2))+(y)/(b^(2))=2]

(x)/(a)+(y)/(b)=a+b(x)/(a^(2))+(y)/(b^(2))=2,a!=0,b!=0

(x)/(a)+(y)/(b)=a^(2)+b^(2) and (x)/(a^(2))+(y)/(b^(2))=a+b

Solve: (x)/(a)+(y)/(b)=a^(2)+b^(2) and (x)/(a^(2))+(y)/(b^(2))=a+b

{:((a^(2))/(x) - (b^(2))/(y) = 0),((a^(2)b)/(x)+(b^(2)a)/(y) = "a + b, where x, y"ne 0.):}

{:((a^(2))/(x) - (b^(2))/(y) = 0),((a^(2)b)/(x)+(b^(2)a)/(y) = "a + b, where x, y"ne 0.):}

Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (a sqrt(2),b) is ax+b sqrt(2)y=(a^(2)+b^(2))sqrt(2)

If y=2/sqrt(a^2-b^2)tan^-1[sqrt((a-b)/(a+b))tan(x/2)] then (d_2y)/(dx^2)|(x=pi/2)|

If y=2/sqrt(a^2-b^2)tan^-1[sqrt((a-b)/(a+b))tan(x/2)] then (d_2y)/(dx^2)|(=),(x=pi/2):|

If two different tangents of y^(2)=4x are the normals to x^(2)=4by, then (a) |b|>(1)/(2sqrt(2)) (b) |b| (1)/(sqrt(2))(d)|b|<(1)/(sqrt(2))