The point of intersection of the asymptotes with the directrices lie on

Consider the following statements : 1. The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle. 2. The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides. Which of the above statements is/are correct ?

Find the equation of the tangents at the ends of the latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and also show that they pass through the points of intersection of the major axis and directrices.

z_(1) and z_(2), lie on a circle with centre at origin. The point of intersection of the tangents at z_(1) and z_(2) is given by

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.