What is 4/3 x^2+4/3 y^2=(x-2)^2 ?

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

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4/3 x^2+4/3 y^2=(x-2)^2

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

(h, k) = (- 6, 0), a = 43, b = 23

Solution steps

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

Rewrite

\frac{4}{3} x^{2} + \frac{4}{3} y^{2} - (x - 2)^{2} = 0

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{( 4 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 0), a = 43, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 0), a = 43, b = 23

9 x^{2} + 25 y^{2} + 36 x - 100 y - 89 = 0

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

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

5 x^{2} + 8 y^{2} = 40

5 x^{2} + 3 y^{2} = 15

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