What is ((x+4)/3)^2+((y+4)/9)^2=(457/81)^2 ?

The solution to ((x+4)/3)^2+((y+4)/9)^2=(457/81)^2 is Ellipse with (h,k)=(-4,-4),a= 457/27 ,b= 457/9

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((x+4)/3)^2+((y+4)/9)^2=(457/81)^2

(\frac{x + 4}{3})^{2} + (\frac{y + 4}{9})^{2} = (\frac{457}{81})^{2}

(h, k) = (- 4, - 4), a = \frac{457}{27}, b = \frac{457}{9}

Solution steps

(\frac{x + 4}{3})^{2} + (\frac{y + 4}{9})^{2} = (\frac{457}{81})^{2}

Rewrite

(\frac{x + 4}{3})^{2} + (\frac{y + 4}{9})^{2} = (\frac{457}{81})^{2}

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{( \frac{457}{27} ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( \frac{457}{9} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, - 4), a = \frac{457}{27}, b = \frac{457}{9}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, - 4), b = \frac{457}{9}, a = \frac{457}{27}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{36} = 1

16 x^{2} + y^{2} + 64 x + 4 y + 52 = 0

7 x^{2} + 4 y^{2} + 24 y = - 8

\frac{x ^{2}}{95} + \frac{y ^{2}}{30} = 1

20 x^{2} + 25 y^{2} = 400

What is ((x+4)/3)^2+((y+4)/9)^2=(457/81)^2 ?
The solution to ((x+4)/3)^2+((y+4)/9)^2=(457/81)^2 is Ellipse with (h,k)=(-4,-4),a= 457/27 ,b= 457/9