What is 4x^2+2y^2=19 ?

The solution to 4x^2+2y^2=19 is Ellipse with (h,k)=(0,0),a=(sqrt(19))/2 ,b=sqrt(19/2)

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4x^2+2y^2=19

4 x^{2} + 2 y^{2} = 19

(h, k) = (0, 0), a = \frac{19}{2}, b = \frac{19}{2}

Solution steps

4 x^{2} + 2 y^{2} = 19

Rewrite

4 x^{2} + 2 y^{2} = 19

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{19}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{19}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{19}{2}, b = \frac{19}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{19}{2}, a = \frac{19}{2}

10 x^{2} + y^{2} - 40 x = 0

4 x^{2} + 16 x + 16 y^{2} - 32 y - 32 = 0

\frac{( x ^{(2)} )}{( 16 )} + \frac{( y ^{(2)} )}{( 7 )} = 1

\frac{( x - 4 ) ^{2}}{5 ^{2}} + \frac{( y - 7 ) ^{2}}{3 ^{2}} = 1

9 x^{2} + 25 y^{2} + 18 x - 50 y = 191

What is 4x^2+2y^2=19 ?
The solution to 4x^2+2y^2=19 is Ellipse with (h,k)=(0,0),a=(sqrt(19))/2 ,b=sqrt(19/2)