What is 16(x-2)^2+25(y+3)^2=124 ?

The solution to 16(x-2)^2+25(y+3)^2=124 is Ellipse with (h,k)=(2,-3),a=(sqrt(31))/2 ,b=(2sqrt(31))/5

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16(x-2)^2+25(y+3)^2=124

16 (x - 2)^{2} + 25 (y + 3)^{2} = 124

(h, k) = (2, - 3), a = \frac{31}{2}, b = \frac{2 31}{5}

Solution steps

16 (x - 2)^{2} + 25 (y + 3)^{2} = 124

Rewrite

16 (x - 2)^{2} + 25 (y + 3)^{2} = 124

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{31}{2} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{2 31}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{31}{2}, b = \frac{2 31}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), a = \frac{31}{2}, b = \frac{2 31}{5}

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What is 16(x-2)^2+25(y+3)^2=124 ?
The solution to 16(x-2)^2+25(y+3)^2=124 is Ellipse with (h,k)=(2,-3),a=(sqrt(31))/2 ,b=(2sqrt(31))/5