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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 2 ) ^{2}}{0} + \frac{( y - 3 ) ^{2}}{4 ^{2}} = 1

x^{2} + 8 y^{2} = 24

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

\frac{x ^{2}}{80} + \frac{y ^{2}}{12} = 1

36 x^{2} + 9 y^{2} = 324

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