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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

(h, k) = (1, 0), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 0), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 0), b = 1, a = 1

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

a^{2} + 2 b^{2} = 1

- 25 x^{2} - 4 y^{2} + 100 = 4

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

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