What is 16x^2+36y^2-96x+144y+144=0 ?

The solution to 16x^2+36y^2-96x+144y+144=0 is Ellipse with (h,k)=(3,-2),a=3,b=2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

16x^2+36y^2-96x+144y+144=0

16 x^{2} + 36 y^{2} - 96 x + 144 y + 144 = 0

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

Solution steps

16 x^{2} + 36 y^{2} - 96 x + 144 y + 144 = 0

Rewrite

16 x^{2} + 36 y^{2} - 96 x + 144 y + 144 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 36 x + 16 y^{2} - 96 y = - 36

4 - 12 x^{2} - 36 y^{2} \geq 0

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

x^{2} + 6 y^{2} = 15

x^{2} = - y^{2} - 8 y

What is 16x^2+36y^2-96x+144y+144=0 ?
The solution to 16x^2+36y^2-96x+144y+144=0 is Ellipse with (h,k)=(3,-2),a=3,b=2