If `y^2=4b(x-c)` and `y^2 =8ax` having common normal then `(a,b,c)` is (A) `(1/2,2,0)` (B) `(1,1,3)` (C) `(1,1,1)` (D) `(1,3,2)`

If x^(2)+3x+3=0 and ax^(2)+bx+1=0 ,a,b in Q have a common root,then value of (3a +b) is equal to : (A) (1)/(3) (B) 1 (C) 2 (D) 4

The orthocentre of the triangle formed by the lines x y=0 and x+y=1 is (a) (1/2,1/2) (b) (1/3,1/3) (c) (0,0) (d) (1/4,1/4)

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) (1/2 ,3/4) (b) (1,3) (c) (3,1) (d) (3/4 ,1/2)

The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at the point (a) (1/2 ,3/4) (b) (1,3) (c) (3,1) (d) (3/4 ,1/2)

The vertex of the parabola y^(2) - 4 y - x + 3 = 0 is a) (-1,3) b) (-1,2) c) (2,-1) d) (3,-1)

The number of normal (s) to the parabola y^(2)=8x through (2,1) is (B) 2(A)1(D)3(C)0

If 4a^2+b^2+2c^2+4a b-6a c-3b c=0, then the family of lines a x+b y+c=0 may be concurrent at point(s) (-1,-1/2) (b) (-1,-1) (-2,-1) (d) (-1,2)

If (x/a)+(y/b)=1 and (x/c)+(y/d)=1 intersect the axes at four concylic points and a^2+c^2=b^2+d^2, then these lines can intersect at, (a , b , c , d >0) (1,1) (b) (1,-1) (2,-2) (d) (3,3)

If ax^2 + 2bx + c = 0 and x^2 + 2b_(1)x + c_(1) = 0 have a common root and a/a_(1), b/b_(1),c/c_(1) are in show that a_(1), b_(1), c_(1) are in G.P.

if |[2a,x_1,y_1],[2b,x_2,y_2],[2c,x_3,y_3]|=(abc)/2!=0 then the area of the triangle whose vertices are (x_1/a,y_1/a),(x_2/b,y_2/b),(x_3/c,y_3/c) is (A) (1/4)abc (B) (1/8)abc (C) 1/4 (D) 1/8