SOLUTION: Which of the following is a foci of the conic section with the equation ? X^2/16-Y^2/4=1 A. (2√5, 0) B. (0, 2√5) C. (2√3, 0)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Which of the following is a foci of the conic section with the equation ? X^2/16-Y^2/4=1 A. (2√5, 0) B. (0, 2√5) C. (2√3, 0)      Log On


   

Question 747274: Which of the following is a foci of the conic section with the equation ?
X^2/16-Y^2/4=1
A. (2√5, 0)
B. (0, 2√5)
C. (2√3, 0)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The formula to determine the focus of a parabola is just the Pythagorean theorem. c is the distance to the focus
c%5E2+=a%5E2+%2B+b%5E2
given: x%5E2%2F16-y%5E2%2F4=1; so, a%5E2=16 =>a=4 and a=-4
and b%5E2=4 =>b=2 and b=-2
then
c%5E2+=4%5E2+%2B+2%5E2
c%5E2+=16+%2B4
c%5E2+=20
c=sqrt%2820%29
c=2sqrt%285%29
since foci at (c,0) => (2sqrt%285%29,0)

answer is: A. (2√5, 0)