Question

@jim_thompson5910
Could you please help me with these problems? I've heard great things about how helpful you are!

1) What is the graph of 4x^2+y^2=16? What are its lines of symmetry? What are the domain and range?

2)What is an equation for the translation of
x^2 + y^2= 10 by 3 units right and 2 units down?

3)What is the standard form of the
equation of an ellipse with foci at
(±3, 0) and co-vertices at (0, ±5)?

4)A hyperbola has vertices (+ or -3, 0) and one focus (5, 0). What is the standard
form of the equation of the hyperbola?

Answer 1

were you able to get anywhere with any of them?

Answer 2

@jim_thompson5910 No not with these unfortunately :/ See these are from a Find the Error Worksheet and they had 10 problems. I was able to do some of them

Answer 3

So you were able to do 6 on your own, but not these 4?

Answer 4

I was able to do 5 of them, but the one I didn't do I did not have enough room to post on here.

Answer 5

If you were to divide both sides of 4x^2+y^2=16 by 16, what would you get?

Answer 6

I think (x^2)/(4) + (y^2)/(16)=1 right?

Answer 7

very good, so what form is that in?

Answer 8

Standard?

Answer 9

have a look at this page

http://www.docstoc.com/docs/32983832/Algebra-2--Section-10-6-Translating-Conic-Sections

Answer 10

Its the formula for an Ellipse?

Answer 11

good, what is the center (h,k)?

What are the values of 'a' and 'b'?

Answer 12

(h,k) is (0,0) I believe and the a is 2 while the b is 4

Answer 13

good on all 3

Answer 14

the standard form

\[\Large \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\]

is an ellipse with center (0,0)

the value of a = 2 and this is the length of the semi-minor axis. Since 'a' corresponds to x, this means the minor axis is horizontal.

the value of b = 4 and this is the length of the semi-major axis. Since 'b' corresponds to y, this means the major axis is vertical.

Answer 15

so the graph looks like this