What is 81x^2+64y^2=25 ?

The solution to 81x^2+64y^2=25 is Ellipse with (h,k)=(0,0),a= 5/9 ,b= 5/8

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81x^2+64y^2=25

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

(h, k) = (0, 0), a = \frac{5}{9}, b = \frac{5}{8}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{9} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{9}, b = \frac{5}{8}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{5}{8}, a = \frac{5}{9}

16 x^{2} + 9 y^{2} = 1

7 x^{2} + 16 y^{2} - 28 x + 128 y + 172 = 0

x^{2} - 16 x + 4 y^{2} - 12 y + 16 = 0

5 x^{2} + 3 y^{2} - 15 = 0

\frac{y ^{2}}{b ^{2}} = 1 - \frac{x ^{2}}{a ^{2}}

What is 81x^2+64y^2=25 ?
The solution to 81x^2+64y^2=25 is Ellipse with (h,k)=(0,0),a= 5/9 ,b= 5/8