What is (((x-1)^2)/4)+(((y-2)^2)/9)=1 ?

The solution to (((x-1)^2)/4)+(((y-2)^2)/9)=1 is Ellipse with (h,k)=(1,2),a=2,b=3

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(((x-1)^2)/4)+(((y-2)^2)/9)=1

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

(h, k) = (1, 2), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 3, a = 2

\frac{y ^{2}}{25} + \frac{x ^{2}}{4} = 1

3 x^{2} + 2 y^{2} = 35

x^{2} + 5 y^{2} - 4 x - 16 = 0

4 x^{(2)} + y^{(2)} = 36

9 x^{2} + 25 y^{2} - 36 x - 50 y + 52 = 0

What is (((x-1)^2)/4)+(((y-2)^2)/9)=1 ?
The solution to (((x-1)^2)/4)+(((y-2)^2)/9)=1 is Ellipse with (h,k)=(1,2),a=2,b=3