What is 4x^2+25y^2+40x-150y+225=0 ?

The solution to 4x^2+25y^2+40x-150y+225=0 is Ellipse with (h,k)=(-5,3),a=5,b=2

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4x^2+25y^2+40x-150y+225=0

4 x^{2} + 25 y^{2} + 40 x - 150 y + 225 = 0

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

Solution steps

4 x^{2} + 25 y^{2} + 40 x - 150 y + 225 = 0

Rewrite

4 x^{2} + 25 y^{2} + 40 x - 150 y + 225 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 (x - 5)^{2} + 9 (y + 2)^{2} = 36

3 x^{2} + 4 y^{2} - 28 x - 16 y + 48 = 0

4 x^{2} + 8 x + 9 (y - 2)^{2} = 32

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

16 x^{2} + 64 x + 4 y^{2} - 8 y + 4 = 0

What is 4x^2+25y^2+40x-150y+225=0 ?
The solution to 4x^2+25y^2+40x-150y+225=0 is Ellipse with (h,k)=(-5,3),a=5,b=2