Question

Hyperbola standard to general form calculator?

a) a²x² - b²y² = 1
b) x²/a² - y²/b² = 1
c) x²+y²=r²
d) x²/r²+y²/r²=1

Answer 1

The student's question involves converting the standard form of a hyperbola's equation to general form, which involves algebraic manipulation. The standard form equation provided can be manipulated by multiplying through by the denominators to achieve the general form of a hyperbola.

Step-by-step explanation:

The question appears to be related to conic sections, specifically the equations of hyperbolas. To convert the standard form of a hyperbola's equation to the general form, you can carry out a few algebraic manipulations.

For example, if we start with the standard form b) x²/a² - y²/b² = 1, you would multiply through by a²b² to get the general form of the hyperbola: a²b²(x²/a²) - a²b²(y²/b²) = a²b², which simplifies to a²x² - b²y² = a²b². Note that the standard form c) x²+y²=r² represents the equation of a circle, not a hyperbola.

If you have additional questions about conic sections or need help with specific calculations, we can cover that as well.