What is x^2+4y^2=15 ?

The solution to x^2+4y^2=15 is Ellipse with (h,k)=(0,0),a=sqrt(15),b=(sqrt(15))/2

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x^2+4y^2=15

x^{2} + 4 y^{2} = 15

(h, k) = (0, 0), a = 15, b = \frac{15}{2}

Solution steps

x^{2} + 4 y^{2} = 15

Rewrite

x^{2} + 4 y^{2} = 15

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 15 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{15}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 15, b = \frac{15}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 15, b = \frac{15}{2}

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0

8 x^{2} + 12 y^{2} = 96

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = \frac{x}{6} + \frac{y}{3}

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{9} = 1

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

What is x^2+4y^2=15 ?
The solution to x^2+4y^2=15 is Ellipse with (h,k)=(0,0),a=sqrt(15),b=(sqrt(15))/2