4x^2+y^2=1

Solution

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

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

Solution steps

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

Rewrite

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

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}

16 x^{2} + 9 y^{2} = 144

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 1

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

2 y^{2} - 16 x = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{36} = 1

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