Statement 1: The line joining the points `(8,-8)a n d(1/2,2),` which are on the parabola `y^2=8x ,` press through the focus of the parabola. Statement 2: Tangents drawn at `(8,-8)` and `(1/2,2),` on the parabola `y^2=4a x` are perpendicular.
(a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Statement 2: The line y=m x+a m+a/m touches y^2=4a(x+a) for all real values of mdot (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: Normal chord drawn at the point (8, 8) of the parabola y^2=8x subtends a right angle at the vertex of the parabola. Statement 2: Every chord of the parabola y^2=4a x passing through the point (4a ,0) subtends a right angle at the vertex of the parabola. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to the line x=1 Statement 2 : A parabola is symmetric about its axis. (a)Both the statements are true and Statements 1 is the correct explanation of Statement 2. (b)Both the statements are true but Statements 1 is not the correct explanation of Statement 2. (c)Statement 1 is true and Statement 2 is false (d)Statement 1 is false and Statement 2 is true

Statement 1: The point of intersection of the tangents at three distinct points A , B ,a n dC on the parabola y^2=4x can be collinear. Statement 2: If a line L does not intersect the parabola y^2=4x , then from every point of the line, two tangents can be drawn to the parabola. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: The length of focal chord of a parabola y^2=8x making on an angle of 60^0 with the x-axis is 32. Statement 2: The length of focal chord of a parabola y^2=4a x making an angle with the x-axis is 4acos e c^2alpha (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: If there exist points on the circle x^2+y^2=a^2 from which two perpendicular tangents can be drawn to the parabola y^2=2x , then ageq1/2 Statement 2: Perpendicular tangents to the parabola meet at the directrix. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa n dQ , then P Q substends a right angle at the origin. Statement 2: Double ordinate equal to twice of latus rectum of a parabola subtends a right angle at the vertex. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1: The value of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1)dot Statement 2: The parabola y=x^2 meets the line x+y=2 at (1,1)dot (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Consider a curve C : y^2-8x-2y-15=0 in which two tangents T_1a n dT_2 are drawn from P(-4,1) . Statement 1: T_1a n dT_2 are mutually perpendicular tangents. Statement 2: Point P lies on the axis of curve Cdot (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Statement 1:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.