Statement 1: If the sum of algebraic distances from point `A(1,1),B(2,3),C(0,2)` is zero on the line `a x+b y+c=0,` then `a+3b+c=0` Statement 2: The centroid of the triangle is (1, 2)

Statement 1 : If the chords of contact of tangents from three points A ,B and C to the circle x^2+y^2=a^2 are concurrent, then A ,B and C will be collinear. Statement 2 : Lines (a_1x+b_1y+c_1)+k(a_2x+b_2y+c_2)=0 alwasy pass through a fixed point for k in R (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: The circumcircle of a triangle formed by the lines x=0,x+y+1=0 and x-y+1=0 also passes through the point (1, 0). Statement 2: The circumcircle of a triangle formed by three tangents of a parabola passes through its focus. (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: 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: 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

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 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1 : The least and greatest distances of the point P(10 ,7) from the circle x^2+y^2-4x-2y-20=0 are 6 units and 15 units, respectively. Statement 2 : A point (x_1,y_1) lies outside the circle S=x^2+y^2+2gx+2fy+c=0 if S_1>0, where S_1=x_1^2+y_1^2+2gx_1+2fy_1+c (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 - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)

The centroid of the triangle formed by the points (1,a), (2,b) and (c^2,-3) by which condition the points lies on the x-axis