What is 9(x-3)^2+4(y-4)^2=36 ?

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

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9(x-3)^2+4(y-4)^2=36

9 (x - 3)^{2} + 4 (y - 4)^{2} = 36

(h, k) = (3, 4), a = 2, b = 3

Solution steps

9 (x - 3)^{2} + 4 (y - 4)^{2} = 36

Rewrite

9 (x - 3)^{2} + 4 (y - 4)^{2} = 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 4), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 4), b = 3, a = 2

\frac{( x - 7 ) ^{2}}{3} + \frac{( y + 11 ) ^{2}}{5} = 1

5 y (y + 4 x) + 4 x^{2} = - 20 (1 - x) y + 5

20 x^{2} + 4 y^{2} = 5

\frac{( x - 5 ) ^{2}}{12} + \frac{( y + 2 ) ^{2}}{16} = 1

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

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