What is 4x^2+9y^2+16x-36y+16=0 ?

The solution to 4x^2+9y^2+16x-36y+16=0 is Ellipse with (h,k)=(-2,2),a=3,b=2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^2+9y^2+16x-36y+16=0

4 x^{2} + 9 y^{2} + 16 x - 36 y + 16 = 0

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

Solution steps

4 x^{2} + 9 y^{2} + 16 x - 36 y + 16 = 0

Rewrite

4 x^{2} + 9 y^{2} + 16 x - 36 y + 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

- 16 - x^{2} - y^{2} \geq 0

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

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{36} = 1

\frac{- 6}{4} = \frac{x ^{2}}{1} + \frac{y ^{2}}{1}

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

What is 4x^2+9y^2+16x-36y+16=0 ?
The solution to 4x^2+9y^2+16x-36y+16=0 is Ellipse with (h,k)=(-2,2),a=3,b=2