What is 4x^2+36y^2-144=0 ?

The solution to 4x^2+36y^2-144=0 is Ellipse with (h,k)=(0,0),a=6,b=2

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4x^2+36y^2-144=0

4 x^{2} + 36 y^{2} - 144 = 0

(h, k) = (0, 0), a = 6, b = 2

Solution steps

4 x^{2} + 36 y^{2} - 144 = 0

Rewrite

4 x^{2} + 36 y^{2} - 144 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = 2

- \frac{6 - x}{4 - y} = - \frac{y}{- 2 - x}

\frac{( ( x + 1 ) ^{2} )}{3} + \frac{( ( y + 1 ) ^{2} )}{4} = 1

2 - 1 = x^{2} + 3 y^{2}

- 25 x^{2} - 4 y^{2} = - 100

\frac{( x + 4 ) ^{2}}{49} + \frac{( y - 4 ) ^{2}}{25} = 1

What is 4x^2+36y^2-144=0 ?
The solution to 4x^2+36y^2-144=0 is Ellipse with (h,k)=(0,0),a=6,b=2