Question

Find the center, vertices, and foci of the ellipse with equation 3x^2 + 7y^2 = 21.
(see attachment for answer choices)

Answer 1

thats for a parabola ... this is an ellipse

Answer 2

ellipse
\[\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1\]

divide by 21 to get RHS to be 1
\[\frac{3x^{2}}{21} + \frac{7y^{2}}{21} = 1\]
reduce
\[\frac{x^{2}}{7} + \frac{y^{2}}{3} = 1\]
\[a = \sqrt{7} , b = \sqrt{3}\]
to find foci, solve for c
where
\[a^{2} = b^{2} + c^{2}\]
\[7 = 3 + c^{2}\]
\[c=2\]

Answer 3

i guess i should add since "a" is under the x^2 , this means the major axis is the "horizontal" or x-axis
it is along this axis that the verticies and foci will be

Answer 4

Oh my gosh, it makes so much more sense now! Thank you so very much!!! You're a lifesaver! <3

Answer 5

yw

Answer 6

so wrong

Answer 7

c^2=a^2-b^2