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}

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

4 (x - 1)^{2} + y^{2} = 36

3 (3 x^{(2)} + 9 y^{(2)} - 2 x - 36) = - 82

\frac{[ ( x - 1 ) ^{2} ]}{25} + \frac{[ ( y + 3 ) ^{2} ]}{9} = 1

25 (x^{2} + 4 x + 4) + 36 (y^{2} + 2 y + 1) = 770

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