(x, y) = (0,0) Discuss the continuity of f(x,y). And show that f(x,y) and f,(x, y) exist at all points (x, y). 4. Find the equation of parabola which has axis parallel to y-axis and which passes...

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Extracted text: (x, y) = (0,0) Discuss the continuity of f(x,y). And show that f(x,y) and f,(x, y) exist at all points (x, y). 4. Find the equation of parabola which has axis parallel to y-axis and which passes through the points (0, 2), (-1,0) and (1, 6). An ellipse circumscribes a rectangle whose sides are given by x the distance between the foci is 4V6 and major axis is along y-axis, then find the equation of the ellipse. +2 and y = +4. If 5. If w = In(x2 + y² + z?), x ue" sin u, y = ue" cos u and z = using chain rule at the point (u, v) = (-2,0). ue", find %3D aw and du aw av 6. Find the directions in which the function f (x,y,z) = In xy + In yz + In xz increase and decrease most rapidly at the point Po(1,1,1). Then find the derivatives of the function in those directions.