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

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

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(x-a)^2+(y-b)^2=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - a ) ^{2}}{1 ^{2}} + \frac{( y - b ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

16 (x - 1)^{2} + 4 (y - 4)^{2} = 64

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{y ^{2}}{9} = 1

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1

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