What is 4x^2+4y^2=100-20x+x^2 ?

The solution to 4x^2+4y^2=100-20x+x^2 is Ellipse with (h,k)=(-10/3 ,0),a= 20/3 ,b=(10)/(sqrt(3))

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4x^2+4y^2=100-20x+x^2

4 x^{2} + 4 y^{2} = 100 - 20 x + x^{2}

(h, k) = (- \frac{10}{3}, 0), a = \frac{20}{3}, b = \frac{10}{3}

Solution steps

4 x^{2} + 4 y^{2} = 100 - 20 x + x^{2}

Rewrite

4 x^{2} + 4 y^{2} - 100 + 20 x - x^{2} = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{10}{3} ) ) ^{2}}{( \frac{20}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{10}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{10}{3}, 0), a = \frac{20}{3}, b = \frac{10}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{10}{3}, 0), a = \frac{20}{3}, b = \frac{10}{3}

6 = x^{2} + 9 y^{2}

1 = \frac{( x - 3 ) ^{2}}{16} + \frac{y ^{2}}{4}

(3 x - 3)^{2} + (- 2 y - 4)^{2} = 43 + 9 + 16

36 x^{2} + 81 y^{2} = 49

49 x^{2} + 16 y^{2} - 784 = 0

What is 4x^2+4y^2=100-20x+x^2 ?
The solution to 4x^2+4y^2=100-20x+x^2 is Ellipse with (h,k)=(-10/3 ,0),a= 20/3 ,b=(10)/(sqrt(3))