What is 9(x-1)^2+4(y+2)^2=36 ?

The solution to 9(x-1)^2+4(y+2)^2=36 is Ellipse with (h,k)=(1,-2),a=2,b=3

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

9 (x - 1)^{2} + 4 (y + 2)^{2} = 36

(h, k) = (1, - 2), a = 2, b = 3

Solution steps

9 (x - 1)^{2} + 4 (y + 2)^{2} = 36

Rewrite

9 (x - 1)^{2} + 4 (y + 2)^{2} = 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 3, a = 2

3 x^{2} + 5 y + 5 y^{2} = 5

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1

49 x^{2} + 9 y^{2} = 16

\frac{( x - 3 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{32} = 1

x^{2} + 4 y^{2} - 20 x + 84 = 0

What is 9(x-1)^2+4(y+2)^2=36 ?
The solution to 9(x-1)^2+4(y+2)^2=36 is Ellipse with (h,k)=(1,-2),a=2,b=3