What is ((x-3)^2)/(21)+((y-2)^2)/(25)=1 ?

The solution to ((x-3)^2)/(21)+((y-2)^2)/(25)=1 is Ellipse with (h,k)=(3,2),a=sqrt(21),b=5

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((x-3)^2)/(21)+((y-2)^2)/(25)=1

\frac{( x - 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{25} = 1

(h, k) = (3, 2), a = 21, b = 5

Solution steps

\frac{( x - 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 21 ) ^{2}} + \frac{( y - 2 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 2), a = 21, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 2), b = 5, a = 21

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

1 - x^{2} - 5 y^{2} > 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{16} = 1

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

36 - 9 x^{2} - 4 y^{2} \geq 0

What is ((x-3)^2)/(21)+((y-2)^2)/(25)=1 ?
The solution to ((x-3)^2)/(21)+((y-2)^2)/(25)=1 is Ellipse with (h,k)=(3,2),a=sqrt(21),b=5