Fill in the blanks:
If the points (3,0) and `(3sqrt(2),2)` lie on the hyperbola `(x^2)/(a^2) - (y^2)/(b^2) = 1`, then its eccentricity is ………….

If it is possible to draw the tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having slope 2, then find its range of eccentricity.

Find the equations of the tangent and normal to the hyperbola x^2/a^2 - y^2/b^2 = 1 at the point (x_0,y_0)

If x/a+y/b=sqrt(2) touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentric angle theta of point of contact.

Fill in the blanks: At (0,0) the curves y =x^2 and y^2 = x

Locus of the point of intersection of the tangents at the points with eccentric angles phi and (pi)/(2) - phi on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is

The eccentricity of the hyperbola 4x^(2)-9y^(2)=36 is :

Fill in the blanks: If f(x) = x^(2//3) , then f'(0) is ……… .

Fill in the blanks. If y=x^(3) then y^(2) is equal to ______.