SOLUTION: Find an equation in standard form for the ellipse with center at (5, 8), horizontal axis of length 10 and passes through the point (6, 4).

Algebra.Com
Question 1204201: Find an equation in standard form for the ellipse with center at (5, 8), horizontal axis of length 10 and passes through the point (6, 4).
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


We can't tell with the given information whether the horizontal axis is the major or minor axis. We can assume it is the major axis and then adjust our results if it turns out that it is the minor axis.

The standard form with center at (5,8) and horizontal major axis of length 10 is



Find b^2 using the given point (6,4) on the ellipse.







Note that b^2=50/3 is less than a^2=25, so the horizontal axis is indeed the major axis.

The standard form of the equation of the ellipse is

ANSWER:


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Find an equation in standard form for the ellipse with center at (5, 8),
horizontal axis of length 10 and passes through the point (6, 4).




Substitute a=10/2=5.  h=5, k=8, x=6, y=4







Multiply through by 25b2.









Edwin
RELATED QUESTIONS

Find in standard form, the equation of an ellipse whose center is at (2,-1) whose major... (answered by lwsshak3)
Find an equation for the ellipse with center(5, 0),foci(5, ±4)and major axis of length... (answered by MathLover1)
Write the standard equation of the ellipse with the given properties Horizontal major... (answered by Edwin McCravy,AnlytcPhil,Plocharczyk)
Find the standard form of the equation of each ellipse. 14. Major axis horizontal with... (answered by ikleyn)
Write the equation of an ellipse, in standard form, with center at (-1,3), vertex at... (answered by Boreal)
Find the standard form of the equation of the ellipse with the given characteristics and... (answered by pavan sai reddy,greenestamps)
Find the standard form of the equation of the ellipse with the given characteristics and... (answered by MathLover1)
Find the equaiton in standard form of the ellipse with center at (4,2) foci (1,2) and... (answered by lwsshak3)
Find an equation in standard form for the ellipse that satisfies the given conditions.... (answered by stanbon,ikleyn)