What is x^2+4y^2-2x+16y+13=0 ?

The solution to x^2+4y^2-2x+16y+13=0 is Ellipse with (h,k)=(1,-2),a=2,b=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2+4y^2-2x+16y+13=0

x^{2} + 4 y^{2} - 2 x + 16 y + 13 = 0

(h, k) = (1, - 2), a = 2, b = 1

Solution steps

x^{2} + 4 y^{2} - 2 x + 16 y + 13 = 0

Rewrite

x^{2} + 4 y^{2} - 2 x + 16 y + 13 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = 2, b = 1

36 x^{2} + 9 y^{2} = 1

4 x^{2} + 9 y^{2} - 40 x + 54 y + 145 = 0

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

\frac{( x - 100 ) ^{2}}{400} + \frac{( y - 90 ) ^{2}}{900} = 1

16 x^{2} + y^{2} = 64

What is x^2+4y^2-2x+16y+13=0 ?
The solution to x^2+4y^2-2x+16y+13=0 is Ellipse with (h,k)=(1,-2),a=2,b=1