What is 150=60x-2x^2+80y-4y^2 ?

The solution to 150=60x-2x^2+80y-4y^2 is Ellipse with (h,k)=(15,10),a=5sqrt(14),b=5sqrt(7)

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150=60x-2x^2+80y-4y^2

150 = 60 x - 2 x^{2} + 80 y - 4 y^{2}

(h, k) = (15, 10), a = 514, b = 57

Solution steps

150 = 60 x - 2 x^{2} + 80 y - 4 y^{2}

Rewrite

150 = 60 x - 2 x^{2} + 80 y - 4 y^{2}

in the form of the standard ellipse equation

\frac{( x - 15 ) ^{2}}{( 5 14 ) ^{2}} + \frac{( y - 10 ) ^{2}}{( 5 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (15, 10), a = 514, b = 57

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (15, 10), a = 514, b = 57

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

25 x^{2} + 4 y^{2} - 50 x + 8 y - 71 = 0

16 x^{2} - 64 x + 25 y^{2} + 100 y = 236

9 x^{2} + 11 y^{2} = 10

16 x^{2} + 36 y^{2} + 32 x + 72 y - 524 = 0

What is 150=60x-2x^2+80y-4y^2 ?
The solution to 150=60x-2x^2+80y-4y^2 is Ellipse with (h,k)=(15,10),a=5sqrt(14),b=5sqrt(7)