A conic in standard form

Tara McConkey
pre calculas-12thgrade
student

Im havign trouble converting the following conic to standard form, i know that the conic is a hyperbola but that is all 16x²-9y²-160x-18y+247=0

could u help me?

Hi Tara,

Since I know, in vague sense, what the standard form will look like, I would gather the terms with an x together, the terms with a y together and move the constant to the right side of the equation.

(16 x² - 160 x) + (-9 y² - 18 y) = -247

I need to complete the squares since I want the x-terms to form a perfect square and the y-terms to form a perfect square. First extract common factors to ensure that the coefficient of x² is 1 and the coefficient of y² is 1.

16(x² - 10 x) -9(y² + 2 y) = -247

Now complete the squares by adding terms to the left side while also adding the same terms to the right side to maintain the equality.

16(x² - 10 x + 25) -9(y² + 2 y + 1) = -247 + 16(25) -9

16(x - 5)² - 9(y + 1)² = 144 Cheers,
Harley Go to Math Central