What is 1/(4x^2+y^2)=1 ?

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

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1/(4x^2+y^2)=1

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

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

Solution steps

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

Rewrite

\frac{1}{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}

4 x^{2} + y^{2} + 8 x > 0

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

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

200 = \frac{1000}{1 + x ^{2} + y ^{2}}

\frac{( x - 8 ) ^{2}}{42} + \frac{( y + 7 ) ^{2}}{16} = 1

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