for parabola `x^2+y^2+2xy−6x−2y+3=0`, the focus is `(a) `(1,-1)` (b) `(-1,1)` (c) `(3,1)` (d) None of these

If the equation (4a-3)x^2+a y^2+6x-2y+2=0 represents a circle, then its centre is a. (3,-1) b. (3,1) c. (-3,1) d. none of these

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 focus of the parabola y^(2) + 6x - 2y + 13 = 0 is at the point a) ((7)/(2), 1) b) ((-1)/(2),1) c) (-2,(1)/(2)) d) (-(7)/(2),1)

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

The coordinates of the focus of the parabola y^2-x-2y+2=0 are a. (5/4,1) b. (1/4,0) c. (1,1) d. none of these

If the equation (4a-3)x^(2)+ay^(2)+6x-2y+2=0 represents a circle,then its centre is a.(3,-1) b.(3,1) c.(-3,1) d.none of these

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then (a) m_1+m_2=0 (b) m_1.m_2=-1 (c) m_1+m_2=1 (d) none of these

What is the focus of the parabola x^2+y^2+2xy−6x−2y+3=0 .