The parabolas `y^2=4ac` and `x^2=4by` intersect orthogonally at point `P(x_1,y_1)` where `x_1,y_1 != 0` provided (A) `b=a^2` (B) `b=a^3` (C) `b^3=a^2` (D) none of these

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

Let the parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point (1,0). Then a+b+c=0a+b=2b-c=1(d)a+c=-2

If normals at two points A(x_1, y_1) and B(x_2, y_2) of the parabola y^2 = 4ax , intersect on the parabola, then y_1, 2sqrt(2)a, y_2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

The tangents to the parabola y^2=4x at the points (1, 2) and (4,4) meet on which of the following lines? (A) x = 3 (B) y = 3 (C) x + y = 4 (D) none of these

The tangents to the parabola y^2=4x at the points (1, 2) and (4,4) meet on which of the following lines? (A) x = 3 (B) y = 3 (C) x + y = 4 (D) none of these

If x^2/a +y^2/b=1 and x^2/c+y^2/d=1 are orthogonal then relation between a , b , c , d is

If x_1 , x_2, x_3 as well as y_1, y_2, y_3 are in A.P., then the points (x_1, y_1), (x_2, y_2), (x_3, y_3) are (A) concyclic (B) collinear (C) three vertices of a parallelogram (D) none of these

If the circle x^2 + y^2 = a^2 intersects the hyperbola xy=c^2 in four points P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4) , then : (A) x_1 + x_2 + x_3 + x_4 = 0 (B) y_1 + y_2 + y_3 + y_4 = 0 (C) x_1 x_2 x_3 x_4= c^4 (D) y_1 y_2 y_3 y_4 = c^4

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these