What is (x^2)/5+(y^2)/4 =1 ?

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

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(x^2)/5+(y^2)/4 =1

\frac{x ^{2}}{5} + \frac{y ^{2}}{4} = 1

(h, k) = (0, 0), a = 5, b = 2

Solution steps

\frac{x ^{2}}{5} + \frac{y ^{2}}{4} = 1

Rewrite

\frac{x ^{2}}{5} + \frac{y ^{2}}{4} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = 2

64 x^{2} + 49 y^{2} = 3136

\frac{x ^{2}}{49} + \frac{y ^{2}}{64} = 1

4 x^{2} + 25 y^{2} + 40 x - 150 y + 225 = 0

4 (x - 5)^{2} + 9 (y + 2)^{2} = 36

3 x^{2} + 4 y^{2} - 28 x - 16 y + 48 = 0

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