Show that the curve for which the normal at every point passes through a fixed point is a circle.

The point on the curve 3y = 6x-5x^3 the normal at Which passes through the origin, is

Show that all chords of a parabola which subtend a right angle at the vertex pass through a fixed point on the axis of the curve.

The locus of midpoints of the chord of the circle x^(2)+y^(2)=25 which pass through a fixed point (4,6) is a circle. The radius of that circle is

Show that the locus of the middle points of chord of an ellipse which paas through a fixed point, is another ellipse

A quadrilateral is inscribed in a parabola y^2=4a x and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

A squadrilateral is inscribed in a parabola y^2=4a x and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

Find the equation of the normal to curve x^2=4y which passes through the point (1, 2).

Find the equation of the normal to curve x^2=4y which passes through the point (1, 2).

Which one of the following curves is the orthogonal trajectory of straight lines passing through a fixed point (a,b) ?

Find the equation of the normal to the curve 2y=x^2 , which passes through the point (2,1).