What is 9x^2+16y^2-90x+256y+1105=0 ?

The solution to 9x^2+16y^2-90x+256y+1105=0 is Ellipse with (h,k)=(5,-8),a=4,b=3

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9x^2+16y^2-90x+256y+1105=0

9 x^{2} + 16 y^{2} - 90 x + 256 y + 1105 = 0

(h, k) = (5, - 8), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} - 90 x + 256 y + 1105 = 0

Rewrite

9 x^{2} + 16 y^{2} - 90 x + 256 y + 1105 = 0

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 8 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 8), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 8), a = 4, b = 3

9 x^{2} + 25 y^{2} - 18 x - 110 y - 116 = 0

33 x^{2} + 13 y^{2} - 396 x + 267 y + 850 = 0

x^{2} + 4 x + 7 y^{2} + y = 0

144 x^{2} + 64 y^{2} + 864 x - 640 y = - 2320

4 x^{2} + 24 x + 9 y^{2} + 18 y + 9 = 0

What is 9x^2+16y^2-90x+256y+1105=0 ?
The solution to 9x^2+16y^2-90x+256y+1105=0 is Ellipse with (h,k)=(5,-8),a=4,b=3