What is 28-4x^2-7y^2>0 ?

The solution to 28-4x^2-7y^2>0 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=2

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28-4x^2-7y^2>0

28 - 4 x^{2} - 7 y^{2} > 0

(h, k) = (0, 0), a = 7, b = 2

Solution steps

28 - 4 x^{2} - 7 y^{2} > 0

Rewrite

28 - 4 x^{2} - 7 y^{2} > 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = 2

2 x^{2} + y^{2} - 2 x + 4 y = 2

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

x^{2} + 8 y^{2} = 32

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

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

What is 28-4x^2-7y^2>0 ?
The solution to 28-4x^2-7y^2>0 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=2