What is (x^2)/(c_{1)^2}=1-(y^2)/(c_{2)^2} ?

The solution to (x^2)/(c_{1)^2}=1-(y^2)/(c_{2)^2} is Ellipse with (h,k)=(0,0),a=c_{1},b=c_{2}

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(x^2)/(c_{1)^2}=1-(y^2)/(c_{2)^2}

\frac{x ^{2}}{c _{1}^{2}} = 1 - \frac{y ^{2}}{c _{2}^{2}}

(h, k) = (0, 0), a = c_{1}, b = c_{2}

Solution steps

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = c_{1}, b = c_{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = c_{1}, b = c_{2}

16 x^{2} + 4 y^{2} - 32 x + 24 y - 12 = 0

x^{2} - 2 x + \frac{y ^{2}}{4} - y \leq 14

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

2 x^{2} - 4 x + y^{2} - 6 y = 9

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

What is (x^2)/(c_{1)^2}=1-(y^2)/(c_{2)^2} ?
The solution to (x^2)/(c_{1)^2}=1-(y^2)/(c_{2)^2} is Ellipse with (h,k)=(0,0),a=c_{1},b=c_{2}