Which of the following correctly represents the coordinates of the foci of the ellipse shown below?

(x-7)^2/4+(y+3)^2/16=1

A. (7±2√3, -3)
B. (7, -3±2√5)
C. (7±2√5, -3)
D. (7, -3±2√3)

am i correct ?? its D i just want to really be sure ...

Question

Which of the following correctly represents the coordinates of the foci of the ellipse shown below?

(x-7)^2/4+(y+3)^2/16=1

  		A. 	(7±2√3, -3)
  		B. 	(7, -3±2√5)
  		C. 	(7±2√5, -3)
  		D. 	(7, -3±2√3)

am i correct ?? its D i just want to really be sure ...

tkhunny · Answer

Center: Eyeball (7,-3)
Half-Length of Major Axis: Eyeball a = 4 (y-direction)
Major Foci: (7,1), (7,-7) -- This eliminates A and C, above.  The foci must be x = 7.
Half-Length of Minor Axis: Eyeball b = 2 (x-direction)
Minor Foci: (9,-3), (5,-3)
Solve for c^2 = a^2 - b^2 = 16 - 4 = 12, so c = $2\sqrt{3}$ -- This eliminates B.

tkhunny · Answer

You just have to wade through it - one piece at a time.  Some things are obvious.  Others are not.

anonymous · Answer

thank you n_n @tkhunny

anonymous · Answer

this really does reassure me n_n

tkhunny · Answer

Next time, you show your work and don't make me do it all.

anonymous · Answer

ohhh okk ill change strategies --- ill state my answer and workn_n to go along with my reasoning

tkhunny · Answer

Good.  If you just say what answer you managed, how does anyone know you didn't just copy it out of the back of the book?  Show your work.  It makes a difference and makes everything better.  :-)