What is x^2+4y^2=36 ?

The solution to x^2+4y^2=36 is Ellipse with (h,k)=(0,0),a=6,b=3

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x^2+4y^2=36

x^{2} + 4 y^{2} = 36

(h, k) = (0, 0), a = 6, b = 3

Solution steps

x^{2} + 4 y^{2} = 36

Rewrite

x^{2} + 4 y^{2} = 36

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = 3

y, x^{2} - 6 x + 9 - 4 y^{2} = 0

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

\frac{x ^{2}}{144} + \frac{y ^{2}}{169} = 1

\frac{x ^{2}}{49} - \frac{y ^{2}}{9} = 1

x^{2} + y = 0

What is x^2+4y^2=36 ?
The solution to x^2+4y^2=36 is Ellipse with (h,k)=(0,0),a=6,b=3