What is 16x^2+9y^2+160x-72y+544=144 ?

The solution to 16x^2+9y^2+160x-72y+544=144 is Ellipse with (h,k)=(-5,4),a=3,b=4

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16x^2+9y^2+160x-72y+544=144

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

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

Solution steps

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

Rewrite

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{4} = 1

7 x^{2} + 18 y^{2} = 63

\frac{( x + 3 ) ^{2}}{100} + \frac{( y + 4 ) ^{2}}{32} = 1

\frac{x ^{2}}{7} + \frac{y ^{2}}{4} = 1

\frac{( x - 2 ) ^{2}}{5} + \frac{( y + 3 ) ^{2}}{9} = 1

What is 16x^2+9y^2+160x-72y+544=144 ?
The solution to 16x^2+9y^2+160x-72y+544=144 is Ellipse with (h,k)=(-5,4),a=3,b=4