What is (x^2)/(81)+(y^2)/(100)=1 ?

The solution to (x^2)/(81)+(y^2)/(100)=1 is Ellipse with (h,k)=(0,0),a=9,b=10

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(x^2)/(81)+(y^2)/(100)=1

\frac{x ^{2}}{81} + \frac{y ^{2}}{100} = 1

(h, k) = (0, 0), a = 9, b = 10

Solution steps

\frac{x ^{2}}{81} + \frac{y ^{2}}{100} = 1

Rewrite

\frac{x ^{2}}{81} + \frac{y ^{2}}{100} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 9, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 10, a = 9

25 (x + 1)^{2} + 16 (y - 3)^{2} = 400

9 y^{2} + 90 y + 4 x^{2} - 16 x + 205 = 0

49 x^{2} + 81 y^{2} = 3969

16 x^{2} - 32 x + 7 y^{2} - 33 - 42 y = 0

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

What is (x^2)/(81)+(y^2)/(100)=1 ?
The solution to (x^2)/(81)+(y^2)/(100)=1 is Ellipse with (h,k)=(0,0),a=9,b=10