Asked by Richard

Give the coordinates of the center, foci, vertices, and asymptotes of the hyperbola with the equation 9x² - 4y² - 90x - 32y = -305.Sketch the graph, and include these points and lines, along with the auxiliary rectangle.

Answers

Answered by mathhelper
First let's complete the square on
9x² - 4y² - 90x - 32y = -305
9(x^2 - 10x + ....) - 4(y^2 + 16t + ....) = -305
9(x^2 - 10x + 25) - 4(y^2 + 16t + 16) = -305 + 9(25) - 4(16)
9(x - 5)^2 - 4(y + 4)^2 = -144
divide by 144
(x-5)^2 / 16 - (y+4)^2 / 36 = -1

centre is (5,-4)
a = 4
b = 6
c^2 = a^2 + b^2
c = 2√13
hyperbola has vertical major axis

I assume that you can build your auxiliary rectangle around (5,-4),
drawing in your asymptotes (the diagonals), and sketching the curve.
Answered by Anonymous
graph
There are no AI answers yet. The ability to request AI answers is coming soon!

Related Questions