What is ((x-4)^2)/(36)+(y^2)/(20)=1 ?

The solution to ((x-4)^2)/(36)+(y^2)/(20)=1 is Ellipse with (h,k)=(4,0),a=6,b=2sqrt(5)

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((x-4)^2)/(36)+(y^2)/(20)=1

\frac{( x - 4 ) ^{2}}{36} + \frac{y ^{2}}{20} = 1

(h, k) = (4, 0), a = 6, b = 25

Solution steps

\frac{( x - 4 ) ^{2}}{36} + \frac{y ^{2}}{20} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{36} + \frac{y ^{2}}{20} = 1

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 0), a = 6, b = 25

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, 0), a = 6, b = 25

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

\frac{x ^{2}}{7} + \frac{y ^{2}}{5} = 1

\frac{( x + 6 ) ^{2}}{100} + \frac{( y - 8 ) ^{2}}{36} = 1

- 7 x^{2} - 9 y^{2} - 63 = 0

\frac{( ( x + 5 ) ^{2} )}{36} + \frac{( ( y - 1 ) ^{2} )}{9} = 1

What is ((x-4)^2)/(36)+(y^2)/(20)=1 ?
The solution to ((x-4)^2)/(36)+(y^2)/(20)=1 is Ellipse with (h,k)=(4,0),a=6,b=2sqrt(5)