Ellipse

[MisterWonderful]

Need help for my exam, which starts in 5 hours from now.
I need an equation for an ellipse, which goes through a point M(8;12) and the distance from the point M to the left focus F1 is 20.
Can someone help me solve this one?

 

[Deleted member 4993]

Need help for my exam, which starts in 5 hours from now.
I need an equation for an ellipse, which goes through a point M(8;12) and the distance from the point M to the left focus F1 is 20.
Can someone help me solve this one?

Do you know the equation of an ellipse? Do you know the co-ordinates of the foci of this ellipse?

Do you know formula for distance between two given points?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[HallsofIvy]

Need help for my exam, which starts in 5 hours from now.
I need an equation for an ellipse, which goes through a point M(8;12) and the distance from the point M to the left focus F1 is 20.
Can someone help me solve this one?

There is no way to do this- there are an infinite number of ellipses satisfying that. Adding the condition that M be a vertex will reduce the number but you would still need to add whether M is a vertex of the major or minor axis.

 

[srmichael]

Also, usually the points that lie on the major axis that the ellipse goes through are referred to as the vertices and those on the minor axis as the co-vertices. However, I have seen some teachers not use the term "co-vertices" and just refer to them as vertices as well, yet if they do this you will have to know if they lie on the major or minor axis so you can come up with the proper equation of the ellipse.

 

[DrPhil]

Need help for my exam, which starts in 5 hours from now.
I need an equation for an ellipse, which goes through a point M(8;12) and the distance from the point M to the left focus F1 is 20.
Can someone help me solve this one?

Better late than never??? [I hope the exam went ok!]

It is important that we have ALL the information given in the question. I would be willing to bet that the ellipse is assumed to be at the origin. Also, the phrase "left focus" implies the major axis is horizontal. In that case, the line MF_1 is the hypotenuse of a right triangle, and Pythagoras lets us find the focus to be at (-8,0). From that, the complete description of the ellipse follows.