What is ((x+11)^2)/(100)+((y-4)^2)/(19^2)=1 ?

The solution to ((x+11)^2)/(100)+((y-4)^2)/(19^2)=1 is Ellipse with (h,k)=(-11,4),a=10,b=19

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((x+11)^2)/(100)+((y-4)^2)/(19^2)=1

\frac{( x + 11 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

(h, k) = (- 11, 4), a = 10, b = 19

Solution steps

\frac{( x + 11 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

Rewrite

\frac{( x + 11 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 11 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 11, 4), a = 10, b = 19

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 11, 4), b = 19, a = 10

4 x^{2} + 3 y^{2} + 4 x = 1

(x - 3)^{2} + 3 (y - 2)^{2} = 2

100 x^{2} + 9 y^{2} = 900

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

\frac{( x - 2 ) ^{2}}{49} + \frac{( y + 4 ) ^{2}}{16} = 1

What is ((x+11)^2)/(100)+((y-4)^2)/(19^2)=1 ?
The solution to ((x+11)^2)/(100)+((y-4)^2)/(19^2)=1 is Ellipse with (h,k)=(-11,4),a=10,b=19