1=4x^2+y^2

Solution

1 = 4 x^{2} + y^{2}

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

Solution steps

1 = 4 x^{2} + y^{2}

Rewrite

1 = 4 x^{2} + y^{2}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 1, a = \frac{1}{2}

x^{2} + 2 y^{2} = 30

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

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 6 ) ^{2}}{121} = 1

36 x^{2} + 16 y^{2} + 180 x - 24 y + 90 = 0

2.4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

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