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Zigmanuir [339]
3 years ago
7

Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1

squared divided by 64 equals 1.
Vertices: (-1, 3), (-1, -13); Foci: (-1, -13), (-1, 3)
Vertices: (3, -1), (-13, -1); Foci: (-13, -1), (3, -1)
Vertices: (-1, 1), (-1, -11); Foci: (-1, -15), (-1, 5)
Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Mathematics
2 answers:
Sphinxa [80]3 years ago
8 0

Answer:

Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)

Step-by-step explanation:

Center at (-5,-1) because of the plus 5 added to the x and the plus 1 added to the y.

a(squared)=36 which means a=6 and a=distance from center to vertices so add and subtract 6 from the x coordinate since this is a horizontal hyperbola, which is (1,-1), (-11,-1). From there you dont need to find the focus since there is only one option for this;

Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)

Gekata [30.6K]3 years ago
5 0

Answer:

Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)

Step-by-step explanation:

Ok so we have 5x\frac{5x^{2} }{36}-\frac{y^{2} }{64}=1

As you know we have the equation of the hyperbola as (x-h)^2/a^2-(y-k)^2/b^2, so the formula of the foci is (h+-c,k) and for vertices (h+-a,k)

then we have to calculate c using pythagoras theorem we have that

a=6 because is the root of 36

b=8 beacause is the root of 64

And then we have that c^{2}=a^{2}+b^{2}

c=\sqrt{36+64}

So the root of 100 is equal to 10

Hence c=10

Using the formula  given before and the equation we know that

h=-5

k=-1

And replacing those values on the equation we have that the foci are

  • (-5-10, -1)=(-15,-1)
  • (-5+10,1)=(5,-1)

And the vertices are:

  • (-5-6, -1)=(-11,-1)
  • (-5+6, 1)= (1,-1)

So the correct answer is D

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