What is 7(x-2004)^2=23-y^2 ?

The solution to 7(x-2004)^2=23-y^2 is Ellipse with (h,k)=(2004,0),a=sqrt(23/7),b=sqrt(23)

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7(x-2004)^2=23-y^2

7 (x - 2004)^{2} = 23 - y^{2}

(h, k) = (2004, 0), a = \frac{23}{7}, b = 23

Solution steps

7 (x - 2004)^{2} = 23 - y^{2}

Rewrite

7 (x - 2004)^{2} - 23 + y^{2} = 0

in the form of the standard ellipse equation

\frac{( x - 2004 ) ^{2}}{( \frac{23}{7} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 23 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2004, 0), a = \frac{23}{7}, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2004, 0), b = 23, a = \frac{23}{7}

\frac{( x - 6 ) ^{2}}{25} + \frac{( y - 7 ) ^{2}}{9} = 1

x^{2} + 2 y^{2} + 8 x - 4 y - 6 = 0

(\frac{y - 4}{16})^{2} + (\frac{x - 6}{4})^{2} = 1

8 x^{2} + y^{2} - 32 x - 16 y = - 16

6 x^{2} + 3 y^{2} + 3 y + 6 x = 15

What is 7(x-2004)^2=23-y^2 ?
The solution to 7(x-2004)^2=23-y^2 is Ellipse with (h,k)=(2004,0),a=sqrt(23/7),b=sqrt(23)