What is 25-x^2-y^2=e^4 ?

The solution to 25-x^2-y^2=e^4 is Ellipse with (h,k)=(0,0),a=sqrt(e^4-25),b=sqrt(e^4-25)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

25-x^2-y^2=e^4

25 - x^{2} - y^{2} = e^{4}

(h, k) = (0, 0), a = e^{4} - 25, b = e^{4} - 25

Solution steps

25 - x^{2} - y^{2} = e^{4}

Rewrite

25 - x^{2} - y^{2} = e^{4}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( e ^{4} - 25 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( e ^{4} - 25 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = e^{4} - 25, b = e^{4} - 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = e^{4} - 25, a = e^{4} - 25

9 x^{2} + y^{2} = 36

25 x^{2} + 49 y^{2} + 100 x - 392 y - 341 = 0

9 x^{2} + 25 y^{2} - 6 x - 25 y - 19 = 0

\frac{x ^{2}}{15} + \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{4} = 1

What is 25-x^2-y^2=e^4 ?
The solution to 25-x^2-y^2=e^4 is Ellipse with (h,k)=(0,0),a=sqrt(e^4-25),b=sqrt(e^4-25)