Question

1) Using the equation find a, b, x1 and y1​

Answer 1

Answer:

• (x₁, y₁) = (2, 1)

• a = 4, b = 2

Step-by-step explanation:

The standard form equation of a hyperbola is

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

Here:

• center (x₁, y₁) = (h, k)

• 'a' is semi-axis and 'b' is semi-conjugate axis 'b'

Given the equation

$\frac{\left(x-2\right)^2}{4^2}-\frac{\left(y-1\right)^2}{2^2}=1$

comparing with the  standard form equation of a hyperbola

(x₁, y₁) = (h, k) = (2, 1)

a = 4, b = 2

Therefore,

• (x₁, y₁) = (2, 1)

• a = 4, b = 2