What is 2((x-6)^2)/3+7((y+4)^2)/4 =1 ?

The solution to 2((x-6)^2)/3+7((y+4)^2)/4 =1 is Ellipse with (h,k)=(6,-4),a=sqrt(3/2),b= 2/(sqrt(7))

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2((x-6)^2)/3+7((y+4)^2)/4 =1

2 \frac{( x - 6 ) ^{2}}{3} + 7 \frac{( y + 4 ) ^{2}}{4} = 1

(h, k) = (6, - 4), a = \frac{3}{2}, b = \frac{2}{7}

Solution steps

2 \cdot \frac{( x - 6 ) ^{2}}{3} + 7 \cdot \frac{( y + 4 ) ^{2}}{4} = 1

Rewrite

2 \frac{( x - 6 ) ^{2}}{3} + 7 \frac{( y + 4 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{( \frac{3}{2} ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( \frac{2}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, - 4), a = \frac{3}{2}, b = \frac{2}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, - 4), a = \frac{3}{2}, b = \frac{2}{7}

4 x^{2} + 3 y^{2} = 9

4 x^{2} + 3 y^{2} = 1

4 x^{2} + y^{2} = 8

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

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 2

What is 2((x-6)^2)/3+7((y+4)^2)/4 =1 ?
The solution to 2((x-6)^2)/3+7((y+4)^2)/4 =1 is Ellipse with (h,k)=(6,-4),a=sqrt(3/2),b= 2/(sqrt(7))