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

The solution to 4(x-1)^2+y^2=36 is Ellipse with (h,k)=(1,0),a=3,b=6

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

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

(h, k) = (1, 0), a = 3, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 0), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 0), b = 6, a = 3

3 (3 x^{(2)} + 9 y^{(2)} - 2 x - 36) = - 82

\frac{[ ( x - 1 ) ^{2} ]}{25} + \frac{[ ( y + 3 ) ^{2} ]}{9} = 1

25 (x^{2} + 4 x + 4) + 36 (y^{2} + 2 y + 1) = 770

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{9} = 1

9 x^{2} - 18 x + 4 y^{2} + 24 y = - 9

What is 4(x-1)^2+y^2=36 ?
The solution to 4(x-1)^2+y^2=36 is Ellipse with (h,k)=(1,0),a=3,b=6