How do you graph an elipse 8x^2 + 32y^2=256?

Question

Step by step instructions please? thanks!

Answer 1

The first thing I'd do is find the x-intercepts and y-intercepts.

When x=0, you're left with 32y^2 = 256.
Hence, y^2 = 8
so y = sqrt(8) = 2sqrt(2)
or y = -sqrt(8) = -2sqrt(2)

This gives you coordinates (0, 2sqrt(2)) and (0, -2sqrt(2))

Similarly, when y=0, you're left with 8x^2 = 256
Hence, x^2 = 32
so x = 4sqrt(2) or -4sqrt(2)

This gives you coordinates (4sqrt(2), 0) and (-4sqrt(2), 0)

Once you have those four coordinates, graphing the ellipse is easy. However, it should be noted that this method runs into trouble if you're dealing with an ellipse that doesn't contain the origin - you'd have to use a different method then.

Answer 2

get the equation to equal one. To do this, divide by 256.

(x^2)/32+(y^2)/8=1
Plug in 0 for x and solve for y, then plug in 0 for y and solve for x. You get:
x=+- 4sqrt2
y=+-2sqrt2

On the x axis, plot points at +4sqrt2 and -4sqrt2.
On the y axis, plot points at +2sqrt2 and -2sqrt2.

Connect the dots to form an oval like shape

Answer 3

If you have like a ti-84 plus silver edition
you can go to the apps program Conics
and select ellipse and then you just enter the values of x and y

Answer 4

Divide by 256

x^2 / 32 + y^2 / 8 = 1
Center (0,0)
Move + - sq rt 32 on x axis and + - sq rt 8 on y- axis to get points.