What is 25x^2+16y^2+100x+32y-284=0 ?

The solution to 25x^2+16y^2+100x+32y-284=0 is Ellipse with (h,k)=(-2,-1),a=4,b=5

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25x^2+16y^2+100x+32y-284=0

25 x^{2} + 16 y^{2} + 100 x + 32 y - 284 = 0

(h, k) = (- 2, - 1), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} + 100 x + 32 y - 284 = 0

Rewrite

25 x^{2} + 16 y^{2} + 100 x + 32 y - 284 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 1), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 1), b = 5, a = 4

4 X^{2} + 8 Y^{2} - 24 X + 32 Y - 12 = 0

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{20} = 1

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

x^{2} + y^{2} = - y^{2} + 4

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

What is 25x^2+16y^2+100x+32y-284=0 ?
The solution to 25x^2+16y^2+100x+32y-284=0 is Ellipse with (h,k)=(-2,-1),a=4,b=5