What is ((x-1)^2)/(81)+((y-2)^2)/(25)=1 ?

The solution to ((x-1)^2)/(81)+((y-2)^2)/(25)=1 is Ellipse with (h,k)=(1,2),a=9,b=5

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((x-1)^2)/(81)+((y-2)^2)/(25)=1

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1

(h, k) = (1, 2), a = 9, b = 5

Solution steps

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 9, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 9, b = 5

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

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

8 x^{2} + 2 y^{2} + 16 x = 1

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

4 x^{2} + 9 y^{2} + 16 x - 18 y - 11 = 0

What is ((x-1)^2)/(81)+((y-2)^2)/(25)=1 ?
The solution to ((x-1)^2)/(81)+((y-2)^2)/(25)=1 is Ellipse with (h,k)=(1,2),a=9,b=5