What is 100y^2+64x^2=6400 ?

The solution to 100y^2+64x^2=6400 is Ellipse with (h,k)=(0,0),a=10,b=8

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100y^2+64x^2=6400

100 y^{2} + 64 x^{2} = 6400

(h, k) = (0, 0), a = 10, b = 8

Solution steps

100 y^{2} + 64 x^{2} = 6400

Rewrite

100 y^{2} + 64 x^{2} = 6400

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = 8

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

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

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{5.9 1 ^{2}} = 1

What is 100y^2+64x^2=6400 ?
The solution to 100y^2+64x^2=6400 is Ellipse with (h,k)=(0,0),a=10,b=8