What is 16x^2+36y^2-256x+448=0 ?

The solution to 16x^2+36y^2-256x+448=0 is Ellipse with (h,k)=(8,0),a=6,b=4

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16x^2+36y^2-256x+448=0

16 x^{2} + 36 y^{2} - 256 x + 448 = 0

(h, k) = (8, 0), a = 6, b = 4

Solution steps

16 x^{2} + 36 y^{2} - 256 x + 448 = 0

Rewrite

16 x^{2} + 36 y^{2} - 256 x + 448 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, 0), a = 6, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, 0), a = 6, b = 4

2 x^{2} + y^{2} = 6

16 (x - 1)^{2} + 25 (y - 2)^{2} = 400

\frac{( x + 2 ) ^{2}}{9} + \frac{y ^{2}}{16} = 1

(\frac{( x - 2 ) ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1

\frac{x}{x ^{2} + y ^{2}} = \frac{3}{2}

What is 16x^2+36y^2-256x+448=0 ?
The solution to 16x^2+36y^2-256x+448=0 is Ellipse with (h,k)=(8,0),a=6,b=4