What is (x^2)/9+(y^2)/c =1 ?

The solution to (x^2)/9+(y^2)/c =1 is Ellipse with (h,k)=(0,0),a=3,b=sqrt(c)

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(x^2)/9+(y^2)/c =1

\frac{x ^{2}}{9} + \frac{y ^{2}}{c} = 1

(h, k) = (0, 0), a = 3, b = c

Solution steps

\frac{x ^{2}}{9} + \frac{y ^{2}}{c} = 1

Rewrite

\frac{x ^{2}}{9} + \frac{y ^{2}}{c} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = c

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = c

16 x^{2} + 36 y^{2} - 256 x + 448 = 0

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

16 (x - 1)^{2} + 25 (y - 2)^{2} = 400

\frac{( x + 2 ) ^{2}}{9} + \frac{y ^{2}}{16} = 1

(\frac{( x - 2 ) ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1

What is (x^2)/9+(y^2)/c =1 ?
The solution to (x^2)/9+(y^2)/c =1 is Ellipse with (h,k)=(0,0),a=3,b=sqrt(c)