What is ((x-8)^2)/4+((y-4)^2)/1 =1 ?

The solution to ((x-8)^2)/4+((y-4)^2)/1 =1 is Ellipse with (h,k)=(8,4),a=2,b=1

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((x-8)^2)/4+((y-4)^2)/1 =1

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

(h, k) = (8, 4), a = 2, b = 1

Solution steps

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

Rewrite

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{2 ^{2}} + \frac{( y - 4 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, 4), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, 4), a = 2, b = 1

4 x^{2} + 9 y^{2} \leq 36

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

\frac{( x + 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{9} = 1

- x^{2} - \frac{y ^{2}}{4} = - 1

x^{2} + 4 y^{2} - 2 x + 16 y + 1 = 0

What is ((x-8)^2)/4+((y-4)^2)/1 =1 ?
The solution to ((x-8)^2)/4+((y-4)^2)/1 =1 is Ellipse with (h,k)=(8,4),a=2,b=1