identify the conic section. if its a parabols give the vertex if its a circle, give the center and radius. if it is an ellipse or a hyperbola, give the center and foci.
again my teacher said the answer is ellipse with center (-4,4), foci at (-4± V3, 4)
but i don't understand how she got it
To determine the type of conic section, as well as its specific characteristics (such as vertex, center, radius, or foci), we need to analyze the given information.
In this case, your teacher has mentioned that the conic section is an ellipse with a center at (-4, 4) and foci at (-4± √3, 4).
To understand how this conclusion is reached, let's break it down step by step:
1. Center: The information provided states that the center of the ellipse is (-4, 4). The center represents the midpoint of the major axis, which is the longest diameter of the ellipse.
2. Foci: For an ellipse, the foci are two fixed points that sit along the major axis and lie inside the ellipse. The foci are symmetrical about the center of the ellipse. Plugging in the values given, we find that the foci are (-4± √3, 4).
Therefore, based on the provided information, your teacher concludes that the conic section is an ellipse with a center at (-4, 4) and foci at (-4± √3, 4).