What is 9x^2+4y^2-18x+24y+9=0 ?

The solution to 9x^2+4y^2-18x+24y+9=0 is Ellipse with (h,k)=(1,-3),a=2,b=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9x^2+4y^2-18x+24y+9=0

9 x^{2} + 4 y^{2} - 18 x + 24 y + 9 = 0

(h, k) = (1, - 3), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 24 y + 9 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 24 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = 3, a = 2

(\frac{( x + 3 )}{16})^{2} + \frac{( y - 5 ) ^{2}}{25} = 1

- 4 x^{2} - 7 y^{2} > - 28

\frac{1}{4} (x - 2)^{2} + \frac{1}{16} (y + 7)^{2} = 1

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

1 x^{2} + 3 y^{2} + 9 x + 9 y - 12 = 0

What is 9x^2+4y^2-18x+24y+9=0 ?
The solution to 9x^2+4y^2-18x+24y+9=0 is Ellipse with (h,k)=(1,-3),a=2,b=3