How do you find the center, vertices, foci and asymptotes of # x^2/7 - y^2/9=1#?

Answer 1

The graph should look like this:
graph{x^2/7-y^2/9=1 [-10, 10, -5, 5]}

#x^2/7-y^2/9=1#
Since we are subtracting, we know that this is a hyperbola. Also, since the fraction with #x^2# is positive, this hyperbola opens to the right and the left. Therefore, equation is in the form #x^2/a^2-y^2/b^2# We know that: #h=0# #k=0# #a=sqrt7# #b=sqrt9# or #3#. #c=sqrt (a^2+b^2)# or #4#. Knowing this, we already know which equations to use: The center is always #(h,k)# The vertices are #(h+a,k)# and #(h-a,k)# The foci are #(h+c,k)# and #(h-c,k)# Since this hyperbola opens sideways, the asymptotes are found by this formula: #y=k+-b/a(x-h)#
Therefore, we know that the center is #(0,0)# The vertices are approximately #(2.645,0)# and #(-2.645,0)# The foci are #(4,0)# and #(-4,0)# The lines of asymptotes are #y=(3sqrt7)/7x# and #y=-(3sqrt7)/7x#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7