What is 16x^2+25y^2+64x+150y-111=0 ?

The solution to 16x^2+25y^2+64x+150y-111=0 is Ellipse with (h,k)=(-2,-3),a=5,b=4

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16x^2+25y^2+64x+150y-111=0

16 x^{2} + 25 y^{2} + 64 x + 150 y - 111 = 0

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

Solution steps

16 x^{2} + 25 y^{2} + 64 x + 150 y - 111 = 0

Rewrite

16 x^{2} + 25 y^{2} + 64 x + 150 y - 111 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

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

8 x^{2} + 2 y^{2} + 16 x = 1

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

What is 16x^2+25y^2+64x+150y-111=0 ?
The solution to 16x^2+25y^2+64x+150y-111=0 is Ellipse with (h,k)=(-2,-3),a=5,b=4