What is 16x^2+25y^2-64x-336=0 ?

The solution to 16x^2+25y^2-64x-336=0 is Ellipse with (h,k)=(2,0),a=5,b=4

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16x^2+25y^2-64x-336=0

16 x^{2} + 25 y^{2} - 64 x - 336 = 0

(h, k) = (2, 0), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 64 x - 336 = 0

Rewrite

16 x^{2} + 25 y^{2} - 64 x - 336 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 0), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 5, b = 4

x^{2} + 2 y^{2} - 4 y = 6

2 x^{2} + 4 y^{2} = 1

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

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

What is 16x^2+25y^2-64x-336=0 ?
The solution to 16x^2+25y^2-64x-336=0 is Ellipse with (h,k)=(2,0),a=5,b=4