What is 3(x-5)^2+4(y+1)^2=6 ?

The solution to 3(x-5)^2+4(y+1)^2=6 is Ellipse with (h,k)=(5,-1),a=sqrt(2),b=sqrt(3/2)

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3(x-5)^2+4(y+1)^2=6

3 (x - 5)^{2} + 4 (y + 1)^{2} = 6

(h, k) = (5, - 1), a = 2, b = \frac{3}{2}

Solution steps

3 (x - 5)^{2} + 4 (y + 1)^{2} = 6

Rewrite

3 (x - 5)^{2} + 4 (y + 1)^{2} = 6

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 1), a = 2, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 1), a = 2, b = \frac{3}{2}

- 8 y^{2} + 72 < 9 x^{2}

4 x^{2} + 9 y^{2} + 16 x + 54 y + 61 = 0

4 x^{2} - 16 x + y^{2} + 2 y + 13 = 0

\frac{( x + 3 ) ^{2}}{49} + \frac{( y + 2 ) ^{2}}{21} = 1

3 x^{2} + 2 y^{2} - 16 x + 15 = 0

What is 3(x-5)^2+4(y+1)^2=6 ?
The solution to 3(x-5)^2+4(y+1)^2=6 is Ellipse with (h,k)=(5,-1),a=sqrt(2),b=sqrt(3/2)