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

The solution to 4(x-1)^2+9y^2=36 is Ellipse with (h,k)=(1,0),a=3,b=2

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

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

(h, k) = (1, 0), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 0), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 0), a = 3, b = 2

\frac{( x ^{2} + 6 x + 9 )}{49} + \frac{( y ^{2} - 2 y + 1 )}{45} = 1

\frac{( y - 5 ) ^{2}}{16} + \frac{( x - 3 ) ^{2}}{4} = 1

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

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

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

What is 4(x-1)^2+9y^2=36 ?
The solution to 4(x-1)^2+9y^2=36 is Ellipse with (h,k)=(1,0),a=3,b=2