What is 4x^2+y^2=16 ?

The solution to 4x^2+y^2=16 is Ellipse with (h,k)=(0,0),a=2,b=4

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4x^2+y^2=16

4 x^{2} + y^{2} = 16

(h, k) = (0, 0), a = 2, b = 4

Solution steps

4 x^{2} + y^{2} = 16

Rewrite

4 x^{2} + y^{2} = 16

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 2

y^{2} = - 8 x

x = y^{2} - 5

y = x^{2} + 2 x - 3

\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1

2 x^{2}

What is 4x^2+y^2=16 ?
The solution to 4x^2+y^2=16 is Ellipse with (h,k)=(0,0),a=2,b=4