What is 16(x-4)^2+25(y+2)^2=400 ?

The solution to 16(x-4)^2+25(y+2)^2=400 is Ellipse with (h,k)=(4,-2),a=5,b=4

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16(x-4)^2+25(y+2)^2=400

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

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

Solution steps

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

Rewrite

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

4 x^{2} + 9 y^{2} \leq 36

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

\frac{( x + 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{9} = 1

What is 16(x-4)^2+25(y+2)^2=400 ?
The solution to 16(x-4)^2+25(y+2)^2=400 is Ellipse with (h,k)=(4,-2),a=5,b=4