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Statement 1:If the point (2a-5,a^2) is o...

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.

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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 : 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 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.

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.

Are the points (3,4) and (2,-6) on the same or opposite sides of the line 3x-4y=8?

Statement 1: Line (x-1)/1=(y-0)/2=(z+2)/(-1) lies in the plane 2x-3y-4z-10=0. Statement 2: if line vec r= vec a+lambda vec b lies in the plane vec r. vec c=n (where n is scalar),then vec b. vec c=0. (a) Both the statements are true, and Statement 2 is the correct explanation for Statement 1. (b) Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1. (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.

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 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: 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.

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
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  6. the diagonals of the parallelogram formed by the the lines a1x+b1y+c1=...

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  13. If the angle between the lines represented by 2x^2+5xy+3y^2+7x+13y-3=0...

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  15. The orthocenter of the triangle formed by the lines xy=0 and x+y=1 is

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