Question

quiz: conic sections hs: algebra 2b m (sequential) / 5:conic no y-intercepts (0, -2) and (0, 2) (0, -4) and (0, 4) (-2, 0) and (2, 0)

Explanation:

Step1: Identify y - intercepts

The y - intercepts of a graph are the points where the graph intersects the y - axis. On the y - axis, the x - coordinate is 0. So we look for the points on the ellipse where \(x = 0\).
From the graph, when \(x=0\), we can see that the ellipse intersects the y - axis at \((0, - 2)\) and \((0,2)\) (by observing the grid and the position of the ellipse relative to the y - axis). Let's analyze the other options:

• Option "no y - intercepts" is wrong because the ellipse does intersect the y - axis.
• Option \((0,-4)\) and \((0,4)\): The ellipse does not reach \(y=\pm4\) on the y - axis.
• Option \((-2,0)\) and \((2,0)\): These are x - intercepts (since \(y = 0\) here), not y - intercepts.

Answer:

(0, -2) and (0, 2)