What is (4x^2)/(19)+(2y^2)/(19)=1 ?

The solution to (4x^2)/(19)+(2y^2)/(19)=1 is Ellipse with (h,k)=(0,0),a=(sqrt(19))/2 ,b=sqrt(19/2)

Popular >

(4x^2)/(19)+(2y^2)/(19)=1

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

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

Solution steps

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

Rewrite

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

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}

2 x - x^{2} - 4 y^{2} - 16 y - 1 = 0

\frac{( x - 4 ) ^{2}}{16} + \frac{y ^{2}}{40.96} = 1

2 x^{2} + 2 y^{2} - 28 y = 0

(x + 2)^{2} 16 + \frac{( y + 2 ) ^{2}}{25} = 1

6 x^{2} + 25 y^{2} - 160 x - 300 y - 300 = 0

What is (4x^2)/(19)+(2y^2)/(19)=1 ?
The solution to (4x^2)/(19)+(2y^2)/(19)=1 is Ellipse with (h,k)=(0,0),a=(sqrt(19))/2 ,b=sqrt(19/2)