What is 9x^2+16y^2-90x-160y+481=0 ?

The solution to 9x^2+16y^2-90x-160y+481=0 is Ellipse with (h,k)=(5,5),a=4,b=3

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9x^2+16y^2-90x-160y+481=0

9 x^{2} + 16 y^{2} - 90 x - 160 y + 481 = 0

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

Solution steps

9 x^{2} + 16 y^{2} - 90 x - 160 y + 481 = 0

Rewrite

9 x^{2} + 16 y^{2} - 90 x - 160 y + 481 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

16 x^{2} + 49 y^{2} = 25

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

x^{2} - 2 x + 2 y^{2} - 8 y + 7 = 0

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

\frac{( x - 23 ) ^{2}}{841} + \frac{( y + 28 ) ^{2}}{484} = 1

What is 9x^2+16y^2-90x-160y+481=0 ?
The solution to 9x^2+16y^2-90x-160y+481=0 is Ellipse with (h,k)=(5,5),a=4,b=3