What is 16x^2+36y^2-224x+208=0 ?

The solution to 16x^2+36y^2-224x+208=0 is Ellipse with (h,k)=(7,0),a=6,b=4

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16x^2+36y^2-224x+208=0

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

(h, k) = (7, 0), a = 6, b = 4

Solution steps

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

Rewrite

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, 0), a = 6, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, 0), a = 6, b = 4

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{5100} = 1

\frac{x ^{2}}{1 2 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

36 x^{2} + 16 y^{2} - 576 = 0

\frac{x ^{2}}{9} + \frac{2 x}{3} + 16 y^{2} - 64 y + \frac{569}{9} = 0

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

What is 16x^2+36y^2-224x+208=0 ?
The solution to 16x^2+36y^2-224x+208=0 is Ellipse with (h,k)=(7,0),a=6,b=4