If the points `(a, 0), (b,0), (0, c)`, and `(0, d)` are concyclic `(a, b, c, d > 0)`, then prove that `ab = cd`.

The points (-a, -b), (0, 0), (a, b) and (a^(2), ab) are

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the line L is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C.

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. The length of the common chord of the parabolas is

Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. Statement 2 : Points A , B , C ,a n dD form an isosceles trapezium or A Ba n dC D meet at Edot Then E A. E B=E C.E D dot

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. The area of cyclic quadrilateral OABC is

Statement 1 :If the lines 2x+3y+19=0 and 9x+6y-17=0 cut the x-axis at A ,B and the y-axis at C ,D , then the points, A , B , C , D are concyclic. Statement 2 : Since O A x O B=O C x O D , where O is the origin, A , B , C , D are concyclic.

Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove that a+d is divisible by 13.