If the curve `C` in the `x y` plane has the equation `x^2+x y+y^2=1,` then the fourth power of the greatest distance of a point on `C` from the origin is___.

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

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

Let f(x,y) be a curve in the x -y plane having the property that distance from the origin of any tangent to the curve is equal to distance of point of contact from the y-axis.It f(1,2)=0, then all such possible curves are

Shortest distance of curve 2x^(2)+5xy+2y^(2)=1 from origin is

Find the distance of the point P(a,b,c) from x-y plane.

If the two lines x+(a-1)y=1 and 2x+a^(2)y=1 , (a in R-{0}) are perpendicular , then the distance of their point of intersection from the origin is

Show that , if x^(2)+y^(2)=1 , then the point (x,y,sqrt(1-x^(2)-y^(2))) is at is distance 1 unit form the origin.

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

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve