What is ((x-10)^2)/(25)+((y-4)^2)/(36)=1 ?

The solution to ((x-10)^2)/(25)+((y-4)^2)/(36)=1 is Ellipse with (h,k)=(10,4),a=5,b=6

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((x-10)^2)/(25)+((y-4)^2)/(36)=1

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

(h, k) = (10, 4), a = 5, b = 6

Solution steps

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

Rewrite

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - 10 ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (10, 4), a = 5, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (10, 4), b = 6, a = 5

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

9 x^{(2)} + 25 y^{(2)} + 18 x + 150 y + 9 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{9} = 1

9 x^{2} + 25 y^{2} + 36 x - 200 y + 211 = 0

8 x^{2} + y^{2} + 4 y = 0

What is ((x-10)^2)/(25)+((y-4)^2)/(36)=1 ?
The solution to ((x-10)^2)/(25)+((y-4)^2)/(36)=1 is Ellipse with (h,k)=(10,4),a=5,b=6