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

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

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9x^2+4y^2-36x=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

- 4 x^{2} - y^{2} + 16 \geq 0

y^{2} = - 4 x^{2} + 16

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

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

\frac{9 ( y ^{2} - 2 )}{16} + z^{2} = 1

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