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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( y + 7 ) ^{2}}{16} + \frac{( x - 5 ) ^{2}}{25} = 1

\frac{4}{x + y i} = x - y i

4 (x + 3)^{2} + y^{2} = 16

2 (1 + 2 y) (y - 2) = - (2 x - 3) (x - 7)

\frac{( x + 1 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{36} = 1

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