What is 4(x-5)^2+9(y+2)^2=36 ?

The solution to 4(x-5)^2+9(y+2)^2=36 is Ellipse with (h,k)=(5,-2),a=3,b=2

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4(x-5)^2+9(y+2)^2=36

4 (x - 5)^{2} + 9 (y + 2)^{2} = 36

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

Solution steps

4 (x - 5)^{2} + 9 (y + 2)^{2} = 36

Rewrite

4 (x - 5)^{2} + 9 (y + 2)^{2} = 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

3 x^{2} + 4 y^{2} - 28 x - 16 y + 48 = 0

4 x^{2} + 8 x + 9 (y - 2)^{2} = 32

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

16 x^{2} + 64 x + 4 y^{2} - 8 y + 4 = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

What is 4(x-5)^2+9(y+2)^2=36 ?
The solution to 4(x-5)^2+9(y+2)^2=36 is Ellipse with (h,k)=(5,-2),a=3,b=2