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

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

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

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

(h, k) = (1, 0), a = 2, b = \frac{3}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 0), a = 2, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 0), a = 2, b = \frac{3}{2}

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

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

x^{2} + 8 y^{2} - 12 x - 16 y - 36 = 0

\frac{( x - 3 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{5} = 1

\frac{( x ^{(2)} )}{( 36 )} + \frac{( y ^{(2)} )}{( 16 )} = 1

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