Show that the equation
`(1)/(x+y-a)+(1)/(x-y+a)+(1)/(y-x+a)=0`
represents a parabola.

Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperbola.

The equation 2y^(2)+3y-4x-3=0 represents a parabola for which

Show that the differential equation that represents the family of all parabolas having their axis of symmetry coincident with the axis of x is y y_2+y1 2=0.

If A(x_1, y_1),B(x_2, y_2),C(x_3, y_3) are the vertices of a triangle, then the equation |x y1x_1y_1 1x_2y_3 1|+|x y1x_1y_1 1x_3y_3 1|=0 represents (a)the median through A (b)the altitude through A (c)the perpendicular bisector of B C (d)the line joining the centroid with a vertex

The equation y^(2)-x^(2)+2x-1=0 , represents

The (x-x_1)(x-x_2)+(y-y_1)(y-y_2=0 represents a circle whose centre is

Show that the equation x^2-2y^2-2x+8y-1=0 represents a hyperbola.

The equation x^(2) + y^(2) - 2xy -1 =0 represents :

Solve the differential equation: e^(x//y)(1-(x)/(y))+(1+e^(x//y)) (dx)/(dy)=0 when x=0, y=1

Solution of the differential equation ((x+y-1)/(x+y-2))(dy)/(dx)=((x+y+1)/(x+y+1)), given that y = 1 when x = 1, is