Question

Given two points M(3, 7) and A(3, -1); which of the following equations is the locus of points T(x, y) such that for lengths MT and AT, MT + AT = 12.
A) (x - 3)^2/12 + (y - 3)^2/4 = 1
B) (x - 3)^2/12 + (y - 3)^2/20 = 1
C) (x - 3)^2/36 + (y - 3)^2/16 = 1
D) (x - 3)^2/20 + (y - 3)^2/36 = 1
E) NOTA
Please show all work! Or if it's logic, please explain!

Answer 1

Are points M and A foci? That's what it seems like to me...

Answer 2

Someone help? Please?

Answer 3

Does look like an ellipse...

Answer 4

Yes, but what afterwards? I'm trying to look through all of the prose in the question and just figure out what M and A are, but I'm not sure. T is obviously the ellipse though...

Answer 5

M and A have the same x-coordinate so the major axis is vertical.
The center is halfway between the foci, so is located at C(3,3), but that is shown in all the equation choices.
Try graphing it and selecting a point T(3,y); you can use the given information and the distance formula to find y.

Answer 6

Yes, M and A are the foci of an ellipse by definition.

Answer 7

Thank you! I finally figured it out! It's D!

Answer 8

The major axis is 12 and therefore, THe two foci to one point on the ellipse equals 12. Again, thanks!

Answer 9

I think I remember a shortcut using the pythagorean theorem, though:
You can pick a point T(x,3) --using covertex on the minor axis instead of vertex on the major axis.. -- and using symmetry, draw an isosceles triangle which you can divide into two equal right triangles.

Answer 10

Hmm, that seems a little dubious. I don't think you can claim right away that the major axis is 12.. I'll check it.

Answer 11

nm, yeah, that checks out. Good job!

Answer 12

Thank you!