Show that the minimum distance from the origin to a point of the curve `x^(2/3)+y^(2/3)=a^(2/3)` is `(a/sqrt(8))`.

The minimum distance of a point on the curve y=x^(2)-4 from the origin is

Show that the lenght of the portion of the tangent to the curve x^(2/3)+y^(2/3)=a^(2/3) at any point of it, intercept between the coordinate axes is contant.

The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

Find the maximum distance of any point on the curve x^2+2y^2+2x y=1 from the origin.

Find the perpendicular distance from the origin of the straight line 3x+4y=5sqrt(2) ,

If p_(1),p_(2) be the lenghts of perpendiculars from origin on the tangent and the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) drawn at any point on it, show that, 4p_(1)^(2)+p_(2)^(2)=a^(2)

Find the equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) at the point (alpha,beta)

Show that the length of the portion of the tangent to the curve x^((2)/(3))+y^((2)/(3))=4 at any point on it, intercepted between the coordinate axis in constant.

Show that the difference of focal distances of any point of the hyperbola 3x^(2) - 4y^(2) = 48 is constant.

The distance between the origin and the normal to the curve y=e^(2x)+x^2 at the point x = 0