What is 16x^2+9y^2-128x-90y+337=0 ?

The solution to 16x^2+9y^2-128x-90y+337=0 is Ellipse with (h,k)=(4,5),a=3,b=4

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16x^2+9y^2-128x-90y+337=0

16 x^{2} + 9 y^{2} - 128 x - 90 y + 337 = 0

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

Solution steps

16 x^{2} + 9 y^{2} - 128 x - 90 y + 337 = 0

Rewrite

16 x^{2} + 9 y^{2} - 128 x - 90 y + 337 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(x + 6)^{2} + \frac{( y + 4 ) ^{2}}{\frac{1}{16}} = 1

4 (x - 1)^{2} + 9 y^{2} = 36

\frac{( x ^{2} + 6 x + 9 )}{49} + \frac{( y ^{2} - 2 y + 1 )}{45} = 1

\frac{( y - 5 ) ^{2}}{16} + \frac{( x - 3 ) ^{2}}{4} = 1

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

What is 16x^2+9y^2-128x-90y+337=0 ?
The solution to 16x^2+9y^2-128x-90y+337=0 is Ellipse with (h,k)=(4,5),a=3,b=4