What is ((x-4)^2)/(25)+((y+7)^2)/(16)=1 ?

The solution to ((x-4)^2)/(25)+((y+7)^2)/(16)=1 is Ellipse with (h,k)=(4,-7),a=5,b=4

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((x-4)^2)/(25)+((y+7)^2)/(16)=1

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

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

Solution steps

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{4 x}{x ^{2} + y ^{2}} = 1

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

144 y^{2} + 63 x^{2} = 9072

\frac{( X - 3 ) ^{2}}{169} + \frac{( Y - 2 ) ^{2}}{144} = 1

What is ((x-4)^2)/(25)+((y+7)^2)/(16)=1 ?
The solution to ((x-4)^2)/(25)+((y+7)^2)/(16)=1 is Ellipse with (h,k)=(4,-7),a=5,b=4