Write the general form for the equations of the hyperbolas?

Question

(x-4)^2/16 - (y+3)^2/4 = 1 

y^2/4 - x^2/25 = 1

 

Answer 1

The general form of hyperbola is Ax² + Cy² + Dx + Ey + F = 0, where A and C have opposite signs.

• The equation is (x - 4)²/16 - (y + 3)²/4 = 1.

(x² - 8x + 16) - 4(y² + 6y + 9) = 16

x² - 8x + 16 - 4y² + 24y + 36 - 16 = 0

x² - 8x - 4y² + 24y + 36 = 0

Now, it is in general form of hyperbola.

• The equation is y²/4 - x²/25 = 1.

25y² - 4x² = 1

- 4x² + 25y² = 1

Now, it is in general form of hyperbola.