In the below figure, the points `A (2,2), B (2sqrt2,0), C(2, -2), D(-2, -2), E(-2, sqrt2,0) and F(-2,2)` are points on a circle, then the area of the shaded path is

Prove that the point A (0,0,0),B(2,0,0), C(1,sqrt3,0) and D(1,1/sqrt3, (2sqrt2)/sqrt3) are the vertices of a regular tetrahedron.

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

The point on the curve x^2=2y which is nearest to the point (0, 5) is(A) (2sqrt(2),4) (B) (2sqrt(2),0) (C) (0, 0) (D) (2, 2)

The radius of the circle passing through the points (1, 2), (5, 2) and (5, -2) is : (A) 5sqrt(2) (B) 2sqrt(5) (C) 3sqrt(2) (D) 2sqrt(2)

The radius of the circle passing through the points (1, 2), (5, 2) and (5, -2) is : (A) 5sqrt(2) (B) 2sqrt(5) (C) 3sqrt(2) (D) 2sqrt(2)