What is ((x+4)^2}{25}+\frac{(y+7)^2)/4 =1 ?

The solution to ((x+4)^2}{25}+\frac{(y+7)^2)/4 =1 is Ellipse with (h,k)=(-4,-7),a=5,b=2

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((x+4)^2}{25}+\frac{(y+7)^2)/4 =1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{4} = 1

(h, k) = (- 4, - 7), a = 5, b = 2

Solution steps

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{4} = 1

Rewrite

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{5 ^{2}} + \frac{( y - ( - 7 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, - 7), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, - 7), a = 5, b = 2

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7 x^{2} + 3 y^{2} - 42 x + 6 y - 39 = 0

What is ((x+4)^2}{25}+\frac{(y+7)^2)/4 =1 ?
The solution to ((x+4)^2}{25}+\frac{(y+7)^2)/4 =1 is Ellipse with (h,k)=(-4,-7),a=5,b=2