What is 16x^2-64x+25y^2+150y+189=0 ?

The solution to 16x^2-64x+25y^2+150y+189=0 is Ellipse with (h,k)=(2,-3),a= 5/2 ,b=2

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16x^2-64x+25y^2+150y+189=0

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

(h, k) = (2, - 3), a = \frac{5}{2}, b = 2

Solution steps

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

Rewrite

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{5}{2}, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), a = \frac{5}{2}, b = 2

2 x^{2} + 3 y^{2} = 12

x^{2} + 4 y^{2} \leq 4

2 x^{2} + 4 y^{2} + 10 x + 9 y - 5 = 0

\frac{( y - 6 ) ^{2}}{36} + \frac{( x + 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{9} + \frac{( y - 4 ) ^{2}}{7} = 1

What is 16x^2-64x+25y^2+150y+189=0 ?
The solution to 16x^2-64x+25y^2+150y+189=0 is Ellipse with (h,k)=(2,-3),a= 5/2 ,b=2