What is 4x^2+y^2+2y-35=0 ?

The solution to 4x^2+y^2+2y-35=0 is Ellipse with (h,k)=(0,-1),a=3,b=6

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4x^2+y^2+2y-35=0

4 x^{2} + y^{2} + 2 y - 35 = 0

(h, k) = (0, - 1), a = 3, b = 6

Solution steps

4 x^{2} + y^{2} + 2 y - 35 = 0

Rewrite

4 x^{2} + y^{2} + 2 y - 35 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 1), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 6, a = 3

5 x^{2} + y^{2} - 20 x + 19 = 0

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{4} = 1

1 x^{2} + 4 y^{2} + 8 x + 9 y - 9 = 0

x^{2} = 9 + 8 y - 4 y^{2}

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{9} = 1

What is 4x^2+y^2+2y-35=0 ?
The solution to 4x^2+y^2+2y-35=0 is Ellipse with (h,k)=(0,-1),a=3,b=6