What is x^2+4y^2-4x-8y+3=0 ?

The solution to x^2+4y^2-4x-8y+3=0 is Ellipse with (h,k)=(2,1),a=sqrt(5),b=(sqrt(5))/2

Popular >

x^2+4y^2-4x-8y+3=0

x^{2} + 4 y^{2} - 4 x - 8 y + 3 = 0

(h, k) = (2, 1), a = 5, b = \frac{5}{2}

Solution steps

x^{2} + 4 y^{2} - 4 x - 8 y + 3 = 0

Rewrite

x^{2} + 4 y^{2} - 4 x - 8 y + 3 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = 5, b = \frac{5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = 5, b = \frac{5}{2}

y^{2} = 9 + \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2}

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

4 x^{2} + y^{2} + 2 y - 15 = 0

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

What is x^2+4y^2-4x-8y+3=0 ?
The solution to x^2+4y^2-4x-8y+3=0 is Ellipse with (h,k)=(2,1),a=sqrt(5),b=(sqrt(5))/2