SOLUTION: Which of the equations below is for an ellipse and which is for a hyperbola? Demonstrate by explaining or showing how you can tell the difference without using a graphing calcula

Algebra ->  Rational-functions -> SOLUTION: Which of the equations below is for an ellipse and which is for a hyperbola? Demonstrate by explaining or showing how you can tell the difference without using a graphing calcula      Log On


   

Question 853215: Which of the equations below is for an ellipse and which is for a hyperbola?
Demonstrate by explaining or showing how you can tell the difference without using a graphing
calculator. You may use the coordinate plane below for sketching, if you choose.
a) 4y2 = 144 + 16x2
b) 4y2 + 16x2 = 144
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Which of the equations below is for an ellipse and which is for a hyperbola?
Demonstrate by explaining or showing how you can tell the difference without using a graphing
calculator. You may use the coordinate plane below for sketching, if you choose.
a) 4y2 = 144 + 16x2
4y^2-16x^2=144
divide by 144
y%5E2%2F36-x%5E2%2F9=1
This is an equation of a hyperbola with vertical transverse axis.
Its standard form: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center.
..
b) 4y2 + 16x2 = 144
divide by 144
y%5E2%2F36%2Bx%5E2%2F9=1
This is an equation of an ellipse with vertical major axis.
Its standard form: %28y-k%29%5E2%2Fa%5E2%2B%28x-h%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center.
..