Question

Name the axis to which the major axis is parallel and find the center of
25(x+5)^(2)+4(y-3)^(2)=100

I think that the center is (-5,3). Is that correct?

I need help with finding out which axis the major axis is parallel to. I do not know how to do it.

Answer 1

center is correct

25(x+5)^(2)+4(y-3)^(2)=100

(x+5)^2 / 4 + (y-3)^2 / 25 = 1

(x+5)^2 / 2^2 + (y-3)^2 / 5^2 = 1

which is bigger , 5 or 2 ?

Answer 2

to make that easier look at
x^2/2^2 + y^2/5^2

Answer 3

5^2 is bigger.

Answer 4

You got it.
now what is x when y = 0 and what is y when x = 0 in
x^2/2^2 + y^2/5^2 = 1

???????????????????????

Answer 5

all I did was move the center to the origin.

Answer 6

x=2 and y=5

Answer 7

x = + or - 2 along x axis
y = + or - 5 along y axis

now which is longer ? :)

Answer 8

Draw x and y axis system and mark those points, then draw an ellipse through them !