What is (x^2)/(C1^2)=1-(y^2)/(C2^2) ?

The solution to (x^2)/(C1^2)=1-(y^2)/(C2^2) is Ellipse with (h,k)=(0,0),a=sqrt(C),b=2sqrt(C)

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(x^2)/(C1^2)=1-(y^2)/(C2^2)

\frac{x ^{2}}{C 1 ^{2}} = 1 - \frac{y ^{2}}{C 2 ^{2}}

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

Solution steps

\frac{x ^{2}}{C \cdot 1 ^{2}} = 1 - \frac{y ^{2}}{C \cdot 2 ^{2}}

Rewrite

\frac{x ^{2}}{C 1 ^{2}} = 1 - \frac{y ^{2}}{C 2 ^{2}}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 1 ) ^{2}}{169} + \frac{( y - 4 ) ^{2}}{144} = 1

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

3 x^{2} + 3 y^{2} - 6 y = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{25} = 1

4 x^{2} - 16 x + 9 y^{2} + 54 y + 61 = 0

What is (x^2)/(C1^2)=1-(y^2)/(C2^2) ?
The solution to (x^2)/(C1^2)=1-(y^2)/(C2^2) is Ellipse with (h,k)=(0,0),a=sqrt(C),b=2sqrt(C)