What is ((x-5)^2)/(16)+((y-2)^2)/(36)=1 ?

The solution to ((x-5)^2)/(16)+((y-2)^2)/(36)=1 is Ellipse with (h,k)=(5,2),a=4,b=6

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((x-5)^2)/(16)+((y-2)^2)/(36)=1

\frac{( x - 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{36} = 1

(h, k) = (5, 2), a = 4, b = 6

Solution steps

\frac{( x - 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{36} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, 2), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, 2), b = 6, a = 4

\frac{( x - 0 ) ^{2}}{36} + \frac{( y - 0 ) ^{2}}{20} = 1

49 x^{2} + 4 y^{2} - 196 = 0

\frac{( x - 5 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{16} = 1

(2 x - y) (3 x - y) = 6 x 2 - 5 x y + y 2

x^{2} + y^{2} = 5 y

What is ((x-5)^2)/(16)+((y-2)^2)/(36)=1 ?
The solution to ((x-5)^2)/(16)+((y-2)^2)/(36)=1 is Ellipse with (h,k)=(5,2),a=4,b=6