What is ((x-1)^2)/(45)+((y-2)^2)/(20)=1 ?

The solution to ((x-1)^2)/(45)+((y-2)^2)/(20)=1 is Ellipse with (h,k)=(1,2),a=3sqrt(5),b=2sqrt(5)

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((x-1)^2)/(45)+((y-2)^2)/(20)=1

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

(h, k) = (1, 2), a = 35, b = 25

Solution steps

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 35, b = 25

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 35, b = 25

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

7 x^{2} + 2 y^{2} - 14 = 0

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} = 1

9 x^{2} + 49 y^{2} + 108 x - 196 y + 79 = 0

What is ((x-1)^2)/(45)+((y-2)^2)/(20)=1 ?
The solution to ((x-1)^2)/(45)+((y-2)^2)/(20)=1 is Ellipse with (h,k)=(1,2),a=3sqrt(5),b=2sqrt(5)