What is 10x^2+4y^2=14 ?

The solution to 10x^2+4y^2=14 is Ellipse with (h,k)=(0,0),a=sqrt(7/5),b=sqrt(7/2)

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10x^2+4y^2=14

10 x^{2} + 4 y^{2} = 14

(h, k) = (0, 0), a = \frac{7}{5}, b = \frac{7}{2}

Solution steps

10 x^{2} + 4 y^{2} = 14

Rewrite

10 x^{2} + 4 y^{2} = 14

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{7}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{5}, b = \frac{7}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{7}{2}, a = \frac{7}{5}

\frac{( x + 6 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

2 x^{2} - 5 x + 3 y^{2} - 4 y = 1

5 x^{2} + 10 y^{2} = 5

3 x^{2} + 3 y^{2} + 36 y = 0

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 7 ) ^{2}}{81} = 1

What is 10x^2+4y^2=14 ?
The solution to 10x^2+4y^2=14 is Ellipse with (h,k)=(0,0),a=sqrt(7/5),b=sqrt(7/2)