What is -9x^2+16y^2-36x-160y+220=0 ?

The solution to -9x^2+16y^2-36x-160y+220=0 is Hyperbola with (h,k)=(-2,5),a=3,b=4

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-9x^2+16y^2-36x-160y+220=0

- 9 x^{2} + 16 y^{2} - 36 x - 160 y + 220 = 0

(h, k) = (- 2, 5), a = 3, b = 4

Solution steps

- 9 x^{2} + 16 y^{2} - 36 x - 160 y + 220 = 0

Rewrite

- 9 x^{2} + 16 y^{2} - 36 x - 160 y + 220 = 0

in the form of a standard hyperbola equation

\frac{( y - 5 ) ^{2}}{3 ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 5), a = 3, b = 4

9 y^{2} - 16 x^{2} - 54 y - 32 x - 79 = 0

\frac{40}{x + y} + \frac{2}{x - y} = 5

\frac{( y - 5 ) ^{2}}{15} - \frac{( x + 4 ) ^{2}}{49} = 1

y^{2} - 4 x^{2} - 24 x - 32 = 0

4 x^{2} - 9 y^{2} + 8 x + 36 y - 68 = 0

What is -9x^2+16y^2-36x-160y+220=0 ?
The solution to -9x^2+16y^2-36x-160y+220=0 is Hyperbola with (h,k)=(-2,5),a=3,b=4