What is 4x^2+y^2-8x+6y+1=0 ?

The solution to 4x^2+y^2-8x+6y+1=0 is Ellipse with (h,k)=(1,-3),a=sqrt(3),b=2sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^2+y^2-8x+6y+1=0

4 x^{2} + y^{2} - 8 x + 6 y + 1 = 0

(h, k) = (1, - 3), a = 3, b = 23

Solution steps

4 x^{2} + y^{2} - 8 x + 6 y + 1 = 0

Rewrite

4 x^{2} + y^{2} - 8 x + 6 y + 1 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 3, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = 23, a = 3

9 (x + 2)^{2} + 4 (y - 1)^{2} - 36 = 0

9 x^{2} + y^{2} - 54 x - 8 y + 88 = 0

2 x^{2} + 4 y^{2} = 12

- 4 y^{2} - z^{2} + 1 = 0

36 x^{2} + 25 y^{2} = 3600

What is 4x^2+y^2-8x+6y+1=0 ?
The solution to 4x^2+y^2-8x+6y+1=0 is Ellipse with (h,k)=(1,-3),a=sqrt(3),b=2sqrt(3)