What is ((x-3)^2)/4+((y-6)^2)/(3/2)=1 ?

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

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((x-3)^2)/4+((y-6)^2)/(3/2)=1

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 6 ) ^{2}}{\frac{3}{2}} = 1

(h, k) = (3, 6), a = 2, b = \frac{3}{2}

Solution steps

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 6 ) ^{2}}{\frac{3}{2}} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 6 ) ^{2}}{\frac{3}{2}} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 6), 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) = (3, 6), a = 2, b = \frac{3}{2}

x^{2} + 9 y^{2} = 5

9 x^{2} + 16 y^{2} + 18 x - 135 = 0

16 x^{2} + 4 y^{2} = 25

x^{2} + 9 y^{2} < 9

x^{2} + 4 y^{2} + 3 x + 2 y - 56 = 0

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