Ellipse based question

Question

How do I find the intersection of an ellipse with coordinate axes? actually my equation is (x+3)^2/9 + (y-1)^2/4 = 1. Now in this whne I put up x=0 then y comes to be 3 but when I put up y=0 then I am getting two values of x both in negative. So which one to prefer. One is - 5.4…. And other is - 0.4…

Answer 1

To get intersecton with x-axis we set y = 0. We get (x + 3)²/9 + 1/4 = 1; (x + 3)² = 27/4; x = - 3 ± 3√3/2.

We have 2 x- intercepts of ellypse: (- 3 + 3√3/2, 0) and ( - 3 - 3√3/2, 0).

To get y-intercepts we set x = 0: 1 + (y - 1)²/4 = 1; (y- 1)²/4 = 0, y = 1.

Ellypse has only 1 y- intercept (0, 1). This means that y-axis is tangent to ellypse.

Answer 2

The ellipse crosses the x axis at both values.