What is 3x^2+4y^2-16x+16=0 ?

The solution to 3x^2+4y^2-16x+16=0 is Ellipse with (h,k)=(8/3 ,0),a= 4/3 ,b= 2/(sqrt(3))

Popular >

3x^2+4y^2-16x+16=0

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

(h, k) = (\frac{8}{3}, 0), a = \frac{4}{3}, b = \frac{2}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{8}{3} ) ^{2}}{( \frac{4}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{8}{3}, 0), a = \frac{4}{3}, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{8}{3}, 0), a = \frac{4}{3}, b = \frac{2}{3}

x^{2} + 2 y^{2} + 4 x + 2 y - 27 = 0

(6 (x)^{2} - 12 x) + ((y)^{2} + 4 y) = - 4

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

x^{2} + 3 y^{2} - 4 x - 23 = 0

25 x^{2} + 9 y^{2} - 200 x + 90 y + 400 = 0

What is 3x^2+4y^2-16x+16=0 ?
The solution to 3x^2+4y^2-16x+16=0 is Ellipse with (h,k)=(8/3 ,0),a= 4/3 ,b= 2/(sqrt(3))