[" (A) "x^(2)+y^(2)-2x-4y+3=0],[" (C) "3(x^(2)+y^(2))-2x-4y+1=0],[" The points with the co-ordinates "(2a,3a),(3b,2b)&" (c,c) are collinear- "],[[" (A) for no value of "a,b,c," (B) for all values of a,b,c "],[" (C) if a,"(c)/(5),b" are in H.P."," (D) if a,"(2)/(5)c,b" are in H.P."]]

If the points A (x,y), B (1,4) and C (-2,5) are collinear, then shown that x + 3y = 13.

If the points A (x,y), B (1,4) and C (-2,5) are collinear, then shown that x + 3y = 13.

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC is:

If the origin and the point P(2,3,4),Q(,1,2,3)R (x,y,z) are coplanar then: a) x-2y-z=0 b) x+2y+z=0 c) x-2y+z=0 d) 2x-2y+z=0

Let each of the circles, S_(1)=x^(2)+y^(2)+4y-1=0 , S_(2)=x^(2)+y^(2)+6x+y+8=0 , S_(3)=x^(2)+y^(2)-4x-4y-37=0 touches the other two. Let P_(1), P_(2), P_(3) be the points of contact of S_(1) and S_(2), S_(2) and S_(3), S_(3) and S_(1) respectively and C_(1), C_(2), C_(3) be the centres of S_(1), S_(2), S_(3) respectively. Q. The co-ordinates of P_(1) are :

Let each of the circles, S_(1)=x^(2)+y^(2)+4y-1=0 , S_(2)=x^(2)+y^(2)+6x+y+8=0 , S_(3)=x^(2)+y^(2)-4x-4y-37=0 touches the other two. Let P_(1), P_(2), P_(3) be the points of contact of S_(1) and S_(2), S_(2) and S_(3), S_(3) and S_(1) respectively and C_(1), C_(2), C_(3) be the centres of S_(1), S_(2), S_(3) respectively. Q. The co-ordinates of P_(1) are :

If y=3x+c is a tangent to the circle x^(2)+y^(2)-2x-4y-5=0, then c is equal to :

The circles x^2+y^2+4x+6y+3=0 and 2(x^2+y^2)+6x+4y+c=0 will cut orthogonally if c is :

If the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

If y= 3x+c is a tangent to the circle x^2+y^2-2x-4y-5=0 , then c is equal to :