What is 9x^2+25y^2=64 ?

The solution to 9x^2+25y^2=64 is Ellipse with (h,k)=(0,0),a= 8/3 ,b= 8/5

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9x^2+25y^2=64

9 x^{2} + 25 y^{2} = 64

(h, k) = (0, 0), a = \frac{8}{3}, b = \frac{8}{5}

Solution steps

9 x^{2} + 25 y^{2} = 64

Rewrite

9 x^{2} + 25 y^{2} = 64

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{8}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{8}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{8}{3}, b = \frac{8}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{8}{3}, b = \frac{8}{5}

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

x^{2} + 2 y^{2} + 2 x - 20 y = - 43

16 x^{2} + 16 y^{2} = 4 y^{2} + 20 y + 25

2 x^{2} + 16 y^{2} = 16

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

What is 9x^2+25y^2=64 ?
The solution to 9x^2+25y^2=64 is Ellipse with (h,k)=(0,0),a= 8/3 ,b= 8/5