Question

Find two functions defined implicitly by the given relation y^2-64x^2=64

Answer 1

Answer: The two functions are

f(x) = sqrt(64x^2+64)

g(x) = -sqrt(64x^2+64)

Graphing these together forms a hyperbola

To get these two functions, we need to solve for y

y^2 - 64x^2 = 64

y^2 = 64x^2 + 64

y = sqrt(64x^2 + 64) or y = -sqrt(64x^2 + 64)

The last line is similar to how x^2 = 9 has two solutions (x = plus or minus 3)