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

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

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

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

(h, k) = (- 4, 2), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 2), a = 2, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 2), a = 2, b = 3

\frac{x ^{2}}{9} + \frac{y ^{2}}{\frac{9}{25}} = 1

y = 4 - \frac{x ^{2}}{4 y}

3 x^{2} + y^{2} - 12 = 0

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

\frac{( x ) ^{2}}{49} + \frac{( y ) ^{2}}{25} = 1

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