Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Writing an equation of an… Given the foci and major axis length

Writing An Equation Of An Given The Foci And Major Axis Length class=

Sagot :

We need to find the equation of the ellipse given the foci and major axis.

The equation is given by:

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

We have the foci points at (2,4) and (2,-6). The distance is 10 units, then the center is equal to half value c=5.

If the length of the major axis is 12.

Major axis length = 2a

Then

12 = 2a

a=12/2

a=6

To find b, we have the next equation:

[tex]\begin{gathered} b^2=a^2-c^2 \\ Replacing \\ b^2=6^2-5^2 \\ b^2=36-25 \\ b^2=11 \\ Solve\text{ for b} \\ b=\sqrt[]{11} \end{gathered}[/tex]

Now, the center c is given by the point (2,-1). This point is in the middle of both foci points

Finally, we can replace on the ellipse equation:

[tex]\begin{gathered} \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1 \\ Replacing,\text{ the result is} \\ \frac{(x-2)^2}{6^2}+\frac{(y-(-1))^2}{(\sqrt[]{11})^2}=1 \end{gathered}[/tex]

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.