What is (36-4x^2-9y^2)=0 ?

The solution to (36-4x^2-9y^2)=0 is Ellipse with (h,k)=(0,0),a=3,b=2

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(36-4x^2-9y^2)=0

(36 - 4 x^{2} - 9 y^{2}) = 0

(h, k) = (0, 0), a = 3, b = 2

Solution steps

(36 - 4 x^{2} - 9 y^{2}) = 0

Rewrite

(36 - 4 x^{2} - 9 y^{2}) = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = 2

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 900 = 0

\frac{x ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

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

25 x^{2} + 16 y^{2} + 100 x + 32 y - 284 = 0

What is (36-4x^2-9y^2)=0 ?
The solution to (36-4x^2-9y^2)=0 is Ellipse with (h,k)=(0,0),a=3,b=2