What is 4x^2+25y^2-200y+300=0 ?

The solution to 4x^2+25y^2-200y+300=0 is Ellipse with (h,k)=(0,4),a=5,b=2

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4x^2+25y^2-200y+300=0

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

(h, k) = (0, 4), a = 5, b = 2

Solution steps

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

Rewrite

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 4 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 4), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 4), a = 5, b = 2

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

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

25 x^{2} + 16 y^{2} - 100 x - 300 = 0

4 x^{2} + 24 x + 25 y^{2} - 300 y + 836 = 0

12 x^{2} = 336 - 7 y^{2}

What is 4x^2+25y^2-200y+300=0 ?
The solution to 4x^2+25y^2-200y+300=0 is Ellipse with (h,k)=(0,4),a=5,b=2