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Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0...

Consider: `L_1:2x+3y+p-3=0` `L_2:2x+3y+p+3=0` where `p` is a real number and `C : x^2+y^2+6x-10 y+30=0` Statement 1 : If line `L_1` is a chord of circle `C ,` then line `L_2` is not always a diameter of circle `Cdot` Statement 2 : If line `L_1` is a a diameter of circle `C ,` then line `L_2` is not a chord of circle `Cdot`
(A) Both the statement are True and Statement 2 is the correct explanation of Statement 1. (B) Both the statement are True but Statement 2 is not the correct explanation of Statement 1. (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: 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.

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: 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 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 number of circles touching lines x+y=1,2x-y=5, and 3x+5y-1=0 is four Statement 2 : In any triangle, four circles can be drawn touching all the three sides of the triangle. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

Statement 1: There are no common tangents between the circle x^2+y^2-4x+3=0 and the parabola y^2=2xdot Statement 2:Given circle and parabola do not intersect. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

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.

Statement 1 : Circles x^2+y^2=144 and x^2+y^2-6x-8y=0 do not have any common tangent. Statement 2 : If two circles are concentric, then they do not have common tangents. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

Statement 1: Each point on the line y-x+12=0 is equidistant from the lines 4y+3x-12=0,3y+4x-24=0 Statement 2: The locus of a point which is equidistant from two given lines is the angular bisector of the two lines. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
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  14. The locus of the centre of a circle which touches externally the circl...

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