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

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

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x^2+(y-c)^2=1

x^{2} + (y - c)^{2} = 1

(h, k) = (0, c), a = 1, b = 1

Solution steps

x^{2} + (y - c)^{2} = 1

Rewrite

x^{2} + (y - c)^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, c), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, c), b = 1, a = 1

4 y^{2} + 9 x^{2} - 24 y - 72 x + 144 = 0

4 x^{2} - 8 x + y^{2} + 6 y = 3

(x + 4)^{2} + (\frac{y - 41}{2})^{2} = \frac{421}{4}

\frac{x ^{2}}{4900} + \frac{y ^{2}}{2500} = 1

x^{2} + y^{2} - \frac{21}{8} x + \frac{19}{4} - \frac{525}{8} = 0

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