Prove that the tangent and normal at any point of an ellipse bisect the external and internal angles between the focal distances of the point

Statement 1 The tangent and normal at any point P on a ellipse bisect the external and internal angles between the focal distance of P.

If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is

If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is

Prove that the tangents drawn from an external point are equal.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of tangent

What is the sum of focal radii of any point on an ellipse equal to ?

Prove that the sum of the focal distance of any point on the ellipse is constant and is equal to the length of the major axis.

Show that the tangent at any point on an ellipse and the tangent at the corresponding point on its auxiliary circle intersect on the major axis.