The Circumcircle of the triangle formed by any three tangents to a parabola passes through

Statement 1: The circumcircle of a triangle formed by the lines x=0,x+y+1=0 and x-y+1=0 also passes through the point (1, 0). Statement 2: The circumcircle of a triangle formed by three tangents of a parabola passes through its focus.

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

The area of the triangle formed by three points on a parabola is how many times the area of the triangle formed by the tangents at these points?

Show that the circumcircle of the triangle formed by three lines x cos alpha_r + y sin alpha_r = p_r, r=1, 2, 3 will pass through the origin if sum_(p_1 p_2) sin (alpha_1 - alpha_2) = 0

Area of the triangle formed by any arbitrary tangents of the hyperbola xy = 4 , with the co-ordinate axes is

The centroid of the triangle formed by the feet of three normals to the parabola y^2=4ax

The equation of the circumcircle of the triangle formed by the lines x=0, y=0, 2x+3y=5, is

The triangle formed by the tangents to a parabola y^2= 4ax at the ends of the latus rectum and the double ordinate through the focus is

The area of the triangle formed by any tangent to the hyperbola x^(2) //a^(2) -y^(2) //b^(2) =1 with its asymptotes is

Tangent at P to the circumcircle of triangle PQR is drawn. If this tangent is parallel to side QR show that Delta PQR is isosceles.