What is 4x^2+24x+25y^2+200y+336=0 ?

The solution to 4x^2+24x+25y^2+200y+336=0 is Ellipse with (h,k)=(-3,-4),a=5,b=2

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4x^2+24x+25y^2+200y+336=0

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

(h, k) = (- 3, - 4), a = 5, b = 2

Solution steps

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

Rewrite

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{5 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 4), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 4), a = 5, b = 2

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

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} = 0

7 x^{2} + 16 y^{2} - 14 x - 64 y - 41 = 0

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

4 x^{(2)} + 9 y^{(2)} = 36

What is 4x^2+24x+25y^2+200y+336=0 ?
The solution to 4x^2+24x+25y^2+200y+336=0 is Ellipse with (h,k)=(-3,-4),a=5,b=2