What is 2x^2+(y-1)^2<= 3 ?

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

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2x^2+(y-1)^2<= 3

2 x^{2} + (y - 1)^{2} \leq 3

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

Solution steps

2 x^{2} + (y - 1)^{2} \leq 3

Rewrite

2 x^{2} + (y - 1)^{2} \leq 3

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

3 x^{2} + y^{2} - 22 x + 22 y = 6

\frac{x ^{2}}{64} + \frac{y ^{2}}{28} = 1

\frac{x ^{2}}{28} + \frac{y ^{2}}{64} = 1

9 x^{2} + y^{2} - 18 x - 2 y + 1 = 0

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