Orthogonal trajectories of the family of curves represented by `x^2+2y^2-y+c=0` is (A) `y^2=a(4x-1)` (B) `y^2=a(4x^2-1)` (C) `x^2=a(4y-1)` (D) `x^2=a(4y^2-1)`

Orthogonal trajectories of the family of curves x^2 + y^2 = c^2

The eccentricity of the conic represented by x^(2)-y^(2)-4x+4y+16=0 is 1(b)sqrt(2)(c)2 (d) (1)/(2)

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0

If the family of curves y=ax^2+b cuts the family of curves x^2+2y^2-y=a orthogonally, then the value of b = (A) 1 (B) 2/3 (C) 1/8 (D) 1/4

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

Q. the equation of image of the pair of lines y=|2x-1| in y-axis is (A) 4x^2-y^2-4x+1=0 (B) 4x^2-y^2+4x+1=0 (C) 4x^2+y^2+4x+1=0 (D) 4x^2+y^2-4x+1=0

Find the angle of intersection of curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0

The locus of the centre of all circles passing through (2, 4) and cutting x^2 + y^2 = 1 orthogonally is : (A) 4x+8y = 11 (B) 4x+8y=21 (C) 8x+4y=21 (D) 4x-8y=21

Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a family of circles. The equation of the circle of the family intersecting the circle x^2+y^2-4x-4y-1=0 orthogonally is (a)x^2+y^2-2x+4y-3=0 (b)x^2+y^2-2x+4y+3=0 (c)x^2+y^2+2x+4y+3=0 (d) x^2+y^2+2x-4y+3=0