Consider the ellipse x^2+4y^2=1 in the xy plane.
1 answer:
Answer:
a. x² +4y² +4z² = 1
b. x² +4y² +z² = 1
Step-by-step explanation:
a. In "intercept form", the given equation can be written as ...
(x/1)² + (y/(1/2))² = 1
When the ellipse is revolved around the x-axis, the z-intercept will match the y-intercept, so the equation becomes ...
(x/1)² + (y/(1/2))² + (z/(1/2))² = 1
x² +4y² +4z² = 1
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b. Likewise, revolving the figure around the y-axis will make the z-intercept the same as the x-intercept. That equation is ...
x² + 4y² +z² = 1
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See the attachments. The first shows revolution about the x-axis; the second shows revolution about the y-axis.
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First we need to find the slope:
Slope formula=
Plug in your given values from the coordinate
Slope =
When we have 2 "-"'s together they turn into a + sign so we add.
Slope =
Slope =
Simplify (in this case divide) the slope:
Slope =
slope-intercept form is:
y=mx+b
Where m=slope
b=y-intercept
So far we have:
y=2x+b
To find b all we have to do is pick any given coordinate and plug it in:
I chose (3,1)
so we plug that in the equation
1=6+b
Now solve for b:
1=6+b
subtract 6 from both sides
b=-5
Final answer:
y=2x-5 (D)
Slope formula=
Plug in your given values from the coordinate
Slope =
When we have 2 "-"'s together they turn into a + sign so we add.
Slope =
Slope =
Simplify (in this case divide) the slope:
Slope =
slope-intercept form is:
y=mx+b
Where m=slope
b=y-intercept
So far we have:
y=2x+b
To find b all we have to do is pick any given coordinate and plug it in:
I chose (3,1)
so we plug that in the equation
1=6+b
Now solve for b:
1=6+b
subtract 6 from both sides
b=-5
Final answer:
y=2x-5 (D)