What is (x-a)^2+(y-(sqrt(a-16)))^2=1 ?

The solution to (x-a)^2+(y-(sqrt(a-16)))^2=1 is Ellipse with (h,k)=(a,sqrt(a-16)),a=1,b=1

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(x-a)^2+(y-(sqrt(a-16)))^2=1

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

(h, k) = (a, a - 16), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (a, a - 16), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (a, a - 16), b = 1, a = 1

3 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

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

6 = 8 x^{2} + y^{2}

4 x^{2} + 7 y^{2} < 28

What is (x-a)^2+(y-(sqrt(a-16)))^2=1 ?
The solution to (x-a)^2+(y-(sqrt(a-16)))^2=1 is Ellipse with (h,k)=(a,sqrt(a-16)),a=1,b=1