How do you write the equation of each conic section ellipse with x-intercepts at (4, 0) and (-4, 0) and y-intercepts at (0, 1) and (0, -1)?

1 Answer
Jan 4, 2016

Answer:

#(x/4)^{2}+(y/1)^{2}=1#, which can also be written as #x^{2}/16+y^{2}=1# or as #x^{2}+16y^{2}=16#.

Explanation:

An equation of an ellipse with #x#-intercepts at #(\pm a,0)# and #y#-intercepts at #(0,pm b)# can be written as #(x/a)^{2}+(y/b)^{2}=1#, or #x^{2}/a^{2}+y^{2}/b^{2}=1#.

You can see that this works by plugging in #y=0# and solving for #x# and plugging in #x=0# and solving for #y#.