The normal to the curve `x^2=4y` passing (1,2) is
(A) `x + y = 3`
(B) `x y = 3`
(C) `x + y = 1`
(D) `x y = 1`

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x - y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x + y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

The normal to the parabola y^2 = -4ax from the point (5a, 2a) are (A) y=x-3a (B) y=-2x+12a (C) y=-3x+33a (D) y=x+3a

The following line(s) is (are) tangent to the curve y=x^2 - x (A) x-y=0 (B) x+y=0 (C) x-y=1 (D) x+y=1

A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-axis at A and B respectively such that BP:AP=2:1 . Given that f(1)=1 . Answer the question:Equation of normal to curve at (1,1) is (A) x-4y+3=0 (B) x-3y+2=0 (C) x-2y+1=0 (D) none of these

The lines parallel to the normal to the curve x y=1 is/are (a) 3x+4y+5=0 (b) 3x-4y+5=0 (c) 4x+3y+5=0 (d) 3y-4x+5=0

The locus of the centre of the circle passing through (1,1) and cutting x^2 + y^2 = 4 orthogonally is : (A) x+y=3 (B) x+2y=3 (C) 2x+y=3 (D) 2x-y=3

Area bounded by the curves y=x and y=x^3 is (A) 1/2 (B) 1 (C) 3/2 (D) 2

Area common to the curves y=sqrt(x) and x=sqrt(y) is (A) 1 (B) 2/3 (C) 1/3 (D) none of these

Let (2,3) be the focus of a parabola and x + y = 0 and x-y= 0 be its two tangents. Then equation of its directrix will be (a) 2x - 3y = 0 (b) 3x +4y = 0 (c) x +y = 5 (d) 12x -5y +1 = 0