Question

If the vertices of an ellipse are at (1, 5) and (1, –5) and (3, 0) is a point on the ellipse, what is the ellipse equation?

(x^2)/(2^2) + (y – 1)^2/(5^2) = 1

(x – 1)^2/(2^2) + (y^2)/(5^2) = 1

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

(x – 1)^2/(5^2) + (y^2)/(2^2) = 1

Answer 1

@freckles or @welshfella

Answer 2

http://www.wolframalpha.com/input/?i=%28x^2%29%2F%282^2%29+%2B+%28y++%E2%80%93++1%29^2%2F%285^2%29+%3D+1

Answer 3

http://www.wolframalpha.com/input/?i=%28x++%E2%80%93++1%29^2%2F%282^2%29+%2B+%28y^2%29%2F%285^2%29+%3D+1

Answer 4

http://www.wolframalpha.com/input/?i=%28x^2%29%2F%282^2%29+%2B+%28y^2%29%2F%285^2%29+%3D+1

Answer 5

http://www.wolframalpha.com/input/?i=%28x++%E2%80%93++1%29^2%2F%285^2%29+%2B+%28y^2%29%2F%282^2%29+%3D+1

Answer 6

aren't vertices the points

Answer 7

@freckles

Answer 8

If we make this traslation:
\[\left\{ \begin{gathered}
x = X + 1 \hfill \\
y = Y \hfill \\
\end{gathered} \right.\]
then the equation of our ellipse, will be:
\[\frac{{{X^2}}}{{{a^2}}} + \frac{{{Y^2}}}{{{b^2}}} = 1\]

Answer 9

what is a?

Answer 10

2

Answer 11

yes!

Answer 12

sorry I have made an error, the right equation is:
\[\frac{{{X^2}}}{{{b^2}}} + \frac{{{Y^2}}}{{{a^2}}} = 1\]

Answer 13

ok

Answer 14

so a is 5^2

Answer 15

or 5

Answer 16

what is b?

Answer 17

2?

Answer 18

starting from the old coordinates, x=3, y=0, we get the new coordinates X, Y using the trslation above, namely:
X=2, Y=0
so substituting into the formula of the ellipse, we get:
(4/b^2)+(0^2/25)=1
so
b=2

Answer 19

traslation*

Answer 20

then the equation of our ellipse, in the XOY system is:
(x^2/4)+(Y^2/25)=1

Answer 21

\[\frac{{{X^2}}}{4} + \frac{{{Y^2}}}{{25}} = 1\]

Answer 22

so its C

Answer 23

now, we have to rewrite that equation using the old coordinates, x, and y

Answer 24

so we have to replace X with x-1 and Y with y. So, what do you get?

Answer 25

(x – 1)^2/(2^2) + (y^2)/(5^2) = 1

Answer 26

please you have to keep in mind the traslation above.
So yes! that's right!

Answer 27

so its B

Answer 28

yes!

Answer 29

thanks