Question

Identify the type of Conic Section that has the equation 16x^2+4y^2=16 and identify its domain and range.

Answer 1

I already know that it is an Ellipse. but I want to know step by step how to get the range and domain of the equation.

Answer 2

@bubbles2000

Answer 3

@mathslover

Answer 4

i wouldn't know sorry :(

Answer 5

@uri

Answer 6

@tkhunny

Answer 7

It has to equal 1, first of all, so divide everything by 16 to get x^2/1 + y^2/4 = 1. Since in an ellipse, the a is always greater than the b, and since the 4 is under the y term, that is your major axis. The formula is x^2/a^2 + y^2/b^2 = 1, or x^2/b^2 + y^2/a^2 = 1. Like I said, since the 4 is under the y term, the y is the major axis with the points located at (0, 2) and (0, -2). That's the range (range is y). The minor axis, the x axis has its vertices at (1, 0) and (-1, 0). Since there are no constants in the numerators with the x^2 and y^2, this is centered at the origin. The domain, btw, is [-1,1]. Range is [2,-2]. I hope this helps!

Answer 8

thanx

Answer 9

@IMstuck can u help me with another question?

Answer 10

The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 24 inches wide and 4 inches deep, how far from the vertex should the microphone be placed?

Answer 11

Let me think on think on this one...

Answer 12

@Miranda122 Post a new thread.

Set it up so that:
Vertex: (0,0)
Point: (-12,4)
Point: (12,4)

Show your work on the other thread when you create it.