The equation of the hyperbola is ![\frac{x^2}{4} -\frac{y^2}{12} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7By%5E2%7D%7B12%7D%20%3D%201)
<h3>How to determine the equation of the graph?</h3>
The points on the graph are given as:
- (2, 0) and (-2, 0)
- (4, 0) and (-4, 0)
- Lines at: x = 1 and x = -1
The hyperbola can be represented as:
![\frac{x^2}{b^2} -\frac{y^2}{a^2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Bb%5E2%7D%20-%5Cfrac%7By%5E2%7D%7Ba%5E2%7D%20%3D%201)
The points (2, 0) and (-2, 0) means that:
![b = \±2](https://tex.z-dn.net/?f=b%20%3D%20%5C%C2%B12)
Square both sides
![b^2 = 4](https://tex.z-dn.net/?f=b%5E2%20%3D%204)
So, we have:
![\frac{x^2}{4} -\frac{y^2}{a^2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7By%5E2%7D%7Ba%5E2%7D%20%3D%201)
Also, we have:
a^2 = c^2 - b^2
Where c = 4
This gives
a^2 = 4^2 - 4
Evaluate
a^2 = 12
Substitute a^2 = 12 in ![\frac{x^2}{4} -\frac{y^2}{a^2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7By%5E2%7D%7Ba%5E2%7D%20%3D%201)
![\frac{x^2}{4} -\frac{y^2}{12} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7By%5E2%7D%7B12%7D%20%3D%201)
Hence, the equation of the hyperbola is ![\frac{x^2}{4} -\frac{y^2}{12} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7By%5E2%7D%7B12%7D%20%3D%201)
Read more about hyperbola at:
brainly.com/question/27799190
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Answer:
7/20
Step-by-step explanation:
Take the time for history assignment and subtract the time for her English assignment
3/5 - 1/4
Get a common denominator of 20
3/5 *4/4 = 12/20
1/4 * 5/5 = 5/20
12/20- 5/20
7/20
Isosceles triangle
ΔPQR:
∠R = ∠Q = (180° - 40°):2 = 70°
2x = 70°⇒ x = 35°
ΔSTV:
SV = TV
![\tt 2x+6 = 3x-6\\\\3x-2x=6+6\\\\x=12](https://tex.z-dn.net/?f=%5Ctt%202x%2B6%20%3D%203x-6%5C%5C%5C%5C3x-2x%3D6%2B6%5C%5C%5C%5Cx%3D12)