Question

The transverse axis of a hyperbola is the x-axis, and the equation of the asymptotes is y=± (4)/(3)x

Answer 1

Given that the transverse axis of a hyperbola is the x-axis, the re-written in the standard form,

a = 3

b = 1

c = 12.

How do you solve for the standard form of the above equation?

It is to be noted that the standard form of a linear equation is given as:

ax + by = c

Rewritten in the normal format,

y=± (4)/(3)x ⇒ y-4 = -3 (x-3)

Simplifying -3(x-3) by applying distributive property and we have:
-3x -3 * -3

Hence

y-4 = -3x -3 * -3

⇒ y-4 = -3x + 9

Collecting like terms on one side of the equation we have

3x + y - 4 = 9
⇒ 3x + y = 9+4
⇒ 3x + y = 12 =  Standard Form

Therefore, in standard from,

a = 3

b = 1

c = 12

See the relevant Graph attached.

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