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

y^{2} + 4 z^{2} = 4

x^{2} + 4 y^{2} - 2 x + 16 y + 13 = 0

36 x^{2} + 9 y^{2} = 1

4 x^{2} + 9 y^{2} - 40 x + 54 y + 145 = 0

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

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