Question

The equation x2 − xy + y2 = 3 represents a "rotated ellipse," that is, an ellipse whose axes are not parallel to the coordinate axes. Find the points at which this ellipse crosses the x-axis.(x, y) = smaller x-value (x, y) = I larger x-value

Answer 1

the points where the ellipse crosses the x- axis are (1.73, 0) and (-1.73, 0)

Explanation:

To find the points at which a graphic crosses the x-axis we need to find the values for x where y = 0.

Therefore, in the equation x²- xy + y² = 3 we are going to make y = 0 and solve for x

x² - xy + y² = 3

x²- x(0) + (0)² = 3

x² = 3

x = ±√3

x₁ = 1.73 and x₂ = -1.73

Therefore, the points where the ellipse crosses the x- axis are (1.73, 0) and (-1.73, 0)