What is 9(x-3)^2+16(y+4)^2=144 ?

The solution to 9(x-3)^2+16(y+4)^2=144 is Ellipse with (h,k)=(3,-4),a=4,b=3

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9(x-3)^2+16(y+4)^2=144

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

(h, k) = (3, - 4), a = 4, b = 3

Solution steps

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

Rewrite

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 4), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 4), a = 4, b = 3

16 x^{2} + 4 y^{2} = 1

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

x^{2} + 6 y^{2} + 14 x - 24 y + 49 = 0

4 x^{2} + 9 y^{2} + 16 x - 18 y - 11 = 0

- y^{2} - x^{2} = 1

What is 9(x-3)^2+16(y+4)^2=144 ?
The solution to 9(x-3)^2+16(y+4)^2=144 is Ellipse with (h,k)=(3,-4),a=4,b=3