What is (x^2)/(81/4)+(y^2)/(25/16)=1 ?

The solution to (x^2)/(81/4)+(y^2)/(25/16)=1 is Ellipse with (h,k)=(0,0),a= 9/2 ,b= 5/4

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(x^2)/(81/4)+(y^2)/(25/16)=1

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

(h, k) = (0, 0), a = \frac{9}{2}, b = \frac{5}{4}

Solution steps

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

Rewrite

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{9}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{9}{2}, b = \frac{5}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{9}{2}, b = \frac{5}{4}

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

x^{2} + 4 y^{2} - 25 = 0

4 x^{2} + y^{2} + 2 y - 35 = 0

5 x^{2} + y^{2} - 20 x + 19 = 0

What is (x^2)/(81/4)+(y^2)/(25/16)=1 ?
The solution to (x^2)/(81/4)+(y^2)/(25/16)=1 is Ellipse with (h,k)=(0,0),a= 9/2 ,b= 5/4