What is ((x-2)^2)/(25)+((y-3)^2)/(16)=1 ?

The solution to ((x-2)^2)/(25)+((y-3)^2)/(16)=1 is Ellipse with (h,k)=(2,3),a=5,b=4

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((x-2)^2)/(25)+((y-3)^2)/(16)=1

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{16} = 1

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

Solution steps

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{9} = 1

4 x^{2} + y^{2} - 24 x - 8 y + 8 = 0

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

4 x^{2} + y^{2} - 24 x + 2 y + 21 = 0

x^{2} + 5 y^{2} = \frac{1}{5}

What is ((x-2)^2)/(25)+((y-3)^2)/(16)=1 ?
The solution to ((x-2)^2)/(25)+((y-3)^2)/(16)=1 is Ellipse with (h,k)=(2,3),a=5,b=4