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

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

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(x-h)^2+(y-k)^2=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - h ) ^{2}}{1 ^{2}} + \frac{( y - k ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

9 x^{2} + 64 y^{2} = 1

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

y + 2 = \frac{6 - ( \frac{6 y + 2 x}{2 + y} )}{2} x

42 x^{2} + 49 y^{2} = 4

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

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