What is 9x^2+4y^2-90x+32y+145=0 ?

The solution to 9x^2+4y^2-90x+32y+145=0 is Ellipse with (h,k)=(5,-4),a=4,b=6

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9x^2+4y^2-90x+32y+145=0

9 x^{2} + 4 y^{2} - 90 x + 32 y + 145 = 0

(h, k) = (5, - 4), a = 4, b = 6

Solution steps

9 x^{2} + 4 y^{2} - 90 x + 32 y + 145 = 0

Rewrite

9 x^{2} + 4 y^{2} - 90 x + 32 y + 145 = 0

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 4), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, - 4), b = 6, a = 4

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{16} = 1

\frac{( x + 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

4 x^{2} - 48 x + 9 y^{2} + 72 y + 144 = 0

\frac{( x - 2.22 ) ^{2}}{2.54} + \frac{y ^{2}}{1.11} = 2

25 x^{2} + 16 y^{2} - 100 x - 64 y - 236 = 0

What is 9x^2+4y^2-90x+32y+145=0 ?
The solution to 9x^2+4y^2-90x+32y+145=0 is Ellipse with (h,k)=(5,-4),a=4,b=6