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

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

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

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

(h, k) = (1, - 2), a = 4, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 5, a = 4

3 X^{2} + 2 Y^{2} = 8

9 x^{2} + 36 y^{2} = 324

5 x^{2} + 9 y^{2} - 20 x - 18 y - 16 = 0

(\frac{( x - 1 )}{6})^{2} + \frac{( y - 3 ) ^{2}}{2} = 1

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

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