What is x^2+4y^2<= 1 ?

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

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x^2+4y^2<= 1

x^{2} + 4 y^{2} \leq 1

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

Solution steps

x^{2} + 4 y^{2} \leq 1

Rewrite

x^{2} + 4 y^{2} \leq 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( X - 5 ) ^{2}}{25} + \frac{( y + 7 ^{2} ) ^{2}}{16} = 1

- x^{2} + \frac{2 x}{21} - \frac{17}{21} = y^{2}

\frac{( x - ( - 0.31 ) ) ^{2}}{3.49} + \frac{y ^{2}}{3.71} = 2

\frac{( x + 4 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{36} = 1

2 x^{2} + y^{2} - 98 = 0

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