Question

Which of the following expresses the coordinates of the foci of the conic section shown below?

Answer 1

Just plug in the values of x and y and see which ones work.

Answer 2

Oh okay! Thanks!

Answer 3

Also, remember these formulas
(x - h)² = 4p(y - k) for vertical parabola
(y - k)² = 4p(x - h) for horizontal parabola

Answer 4

Well, this is the equation of an ellipse. The foci is located c units away from the center. So first we would need to find c. In the case of an ellipse, c = √(a^2 - b^2) In an ellipse, a^2 is the higher of the two denominators, namely 49 in your problem while b is 25. So c = √(24). So the foci is + or - √24 units from the center. Now we need to find the center. The coordinates of the center follow the form of (x-h) and (y-k) where h is the shift on the x-axis and k is the shift on y-axis. This problem gives (x+2) and (y-1). So the shift along the x-axis is (x-(-2)) and the shift along the y-axis is (y-(1)). So the center is at (-2,1). The final bit of info needed is does the ellipse flatten along thex-axis or the y-axis. This is found by seeing which variable has the higher number in its denominator. In your problem, the x variable term has a higher denominator, meaning the ellipse flattens parallel to the x-axis. Since it flattens along the x-axis, my foci are left √(24) and right √(24) units from the center. Simplifying √(24) gives us 2√(6). So the cooridnates are (-2 +/- 2√(6) , 1)

Answer 5

Okay after that I understand! I'm going to practice it on a few more problems, thank you guys for helping~(:

Answer 6

Good Luck!