What is 6=4x^2+y^2+1 ?

The solution to 6=4x^2+y^2+1 is Ellipse with (h,k)=(0,0),a=(sqrt(5))/2 ,b=sqrt(5)

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6=4x^2+y^2+1

6 = 4 x^{2} + y^{2} + 1

(h, k) = (0, 0), a = \frac{5}{2}, b = 5

Solution steps

6 = 4 x^{2} + y^{2} + 1

Rewrite

6 - 4 x^{2} - y^{2} - 1 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{2}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = \frac{5}{2}

9 y^{2} = 25 (3 - x) (3 + x)

16 (x - 1)^{2} + 25 (y - 4)^{2} = 400

49 x^{2} + 25 y^{2} = 1225

4 (x - 1)^{2} + 25 (y - 3)^{2} = 1

(\frac{4}{9 - x ^{2} - y ^{2}})^{2} = 16

What is 6=4x^2+y^2+1 ?
The solution to 6=4x^2+y^2+1 is Ellipse with (h,k)=(0,0),a=(sqrt(5))/2 ,b=sqrt(5)