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

The curve for which the normal at every point passes through a fixed point (h,k) is

The curve for which the normal at every point passes through a fixed point is a (A) parabola (B) hyperbola (C) ellipse (D) circle

A family of circles passing through the points (3, 7) and (6, 5) cut the circle x^2 + y^2 - 4x-6y-3=0 . Show that the lines joining the intersection points pass through a fixed point and find the coordinates of the point.

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

A quadrilateral is inscribed in a parabola y^(2)=4ax 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.

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