What is 1x^2+2y^2=9 ?

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

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1x^2+2y^2=9

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 3 ) ^{2}}{64} + \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + y^{2} + 48 x + 128 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{16} = 1

(x - 1)^{2} + (2 y + 4)^{2} = 16

64 xx - 256 x + 81 yy + 810 y = 2903

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