The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is `x-y+1=0` is (a) `x^2+y^2-2x y-4x-4y-4=0` (b) `x^2+y^2-2x y+4x-4y-4=0` (c)`x^2+y^2+2x y-4x+4y-4=0` (d)`x^2+y^2+2x y-4x-4y+4=0`

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

The equation of the parabola whose vertex is at (0,0) and focus is the point of intersection of x+y=2,2x-y=4 is

The equation of the circle passing through the point (1,1) and having two diameters along the pair of lines x^2-y^2-2x+4y-3=0 is a. x^2+y^2-2x-4y+4=0 b. x^2+y^2+2x+4y-4=0 c. x^2+y^2-2x+4y+4=0 d. none of these

The vertex of the parabola x^(2)+y^(2)-2xy-4x-4y+4=0 is at

Equation of the rectangular hyperbola whose focus is (1,-1) and the corresponding directrix is x-y+1=0 . a. x^(2)-y^(2)=1 b. xy=1 c. 2xy-4x+4y+1=0 d. 2xy+4x-4y-1=0

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