Show that for any point of the curve `x^2 - y^2 = a^2` the segment of the normal from the point to the point of intersection of the normal with the x-axis is equal to the distance of the point from the origin.

Show that for any point of the curve x^(2)-y^(2)=a^(2) the segment of the normal from x^(2)-y^(2)=a^(2) the point of intersection of the normal with the point of intersection of the normal with the x-axis is equal to the distance of the point from the origin.

Find the locus of a point whose distance from x-axis is equal the distance from the point (1, -1, 2) :

At any point on the curve y=f(x) ,the sub-tangent, the ordinate of the point and the sub-normal are in

Find whether the line 2x+y=3 cuts the curve 4x^(2)+y^(2)=5. Obtain the equations of the normals at the points of intersection.

The point of intersection of normals to the parabola y^(2)=4x at the points whose ordinmes are 4 and 6 is

The slopes of the normals to the parabola y^(2)=4ax intersecting at a point on the axis of the a distance 4a from its vertex are in

Equation of the normal to the curve y=-sqrt(x)+2 at the point of its intersection with the curve y=tan(tan-1x) is

The equation of the normal to the curve y=x(2-x) at the point (2, 0) is

Find the locus of a point whose distance from the point (1,2) is equal to its distance from axis of y.

If the tangent to the curve y= e^x at a point (c, e^c) and the normal to the parabola, y^2 = 4x at the point (1,2) intersect at the same point on the x-axis then the value of c is ____________.