Question

URGENT!!!!

Answer 1

The equation of the hyperbola in standard form is $\frac{(y-4)^{2}}{100}-\frac{(x-1)^{2}}{64}=1$

Step-by-step explanation:

Let us revise the equation of the hyperbola

The standard form of the equation of a hyperbola with  center (h , k) and transverse axis parallel to the y-axis is  $\frac{(y-k)^{2}}{a^{2}}-\frac{(x-h)^{2}}{b^{2}}=1$

• The length of the transverse axis is 2a  
• The length of the conjugate axis is 2b  

∵ The center of the hyperbola is (1 , 4)

∴ h = 1 and k = 4

∵ The transverse axis is parallel to the y-axis

∴ The form of the equation is  $\frac{(y-k)^{2}}{a^{2}}-\frac{(x-h)^{2}}{b^{2}}=1$

∴ The length of the transverse axis is 2a  

∵ The length of the transverse axis is 20 units

- Equate 2a by 20 to find a

∴ 2a = 20

- Divide both sides by 2

∴ a = 10

∵ The length of the conjugate axis is 2b

∵ The length of the conjugate axis is 16

- Equate 2b by 16 to find b

∴ 2b = 16

- Divide both sides by 2

∴ b = 8

- Substitute the values of h, k, a, and b in the form of the equation

∴  $\frac{(y-4)^{2}}{(10)^{2}}-\frac{(x-1)^{2}}{(8)^{2}}=1$

∴  $\frac{(y-4)^{2}}{100}-\frac{(x-1)^{2}}{64}=1$

The equation of the hyperbola in standard form is $\frac{(y-4)^{2}}{100}-\frac{(x-1)^{2}}{64}=1$

Learn more:

You can learn more about the hyperbola in brainly.com/question/4054269

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