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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{7. 5 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1

9 y^{2} = 36 - 4 x^{2}

\frac{x ^{2}}{98} + \frac{y ^{2}}{2} = 1

x^{2} + 4 y^{2} + 10 x - 8 y + 13 = 0

x^{2} + 4 y^{2} + 12 x = 0

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