What is ((x-4)^2)/9+((y-2)^2)/(25)=1 ?

The solution to ((x-4)^2)/9+((y-2)^2)/(25)=1 is Ellipse with (h,k)=(4,2),a=3,b=5

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((x-4)^2)/9+((y-2)^2)/(25)=1

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{25} = 1

(h, k) = (4, 2), a = 3, b = 5

Solution steps

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{3 ^{2}} + \frac{( y - 2 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 2), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 2), b = 5, a = 3

(y - 6)^{2} = 23 - \frac{23 ( x - 3 ) ^{2}}{39}

\frac{x ^{2}}{1.58 7 ^{2}} + \frac{y ^{2}}{0.9 9 ^{2}} = 1

9 \cdot (x - 1)^{2} + 4 \cdot y^{2} = 36

4 x^{2} + 9 y^{2} - 144 = 0

3 x^{2} + 2 y^{2} - 8 = 0

What is ((x-4)^2)/9+((y-2)^2)/(25)=1 ?
The solution to ((x-4)^2)/9+((y-2)^2)/(25)=1 is Ellipse with (h,k)=(4,2),a=3,b=5