What is ((x-4)^2)/9+((y+2)^2)/(25)=1 ?

The solution to ((x-4)^2)/9+((y+2)^2)/(25)=1 is Ellipse with (h,k)=(4,-2),a=3,b=5

Popular >

((x-4)^2)/9+((y+2)^2)/(25)=1

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{25} = 1

(h, k) = (4, - 2), a = 3, b = 5

Solution steps

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 5, a = 3

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

2 x^{2} - 6 < - 6 y^{2}

\frac{x ^{2}}{49} + \frac{y ^{2}}{169} = 1

(- y - 6)^{2} + 8 x^{2} = 64

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

What is ((x-4)^2)/9+((y+2)^2)/(25)=1 ?
The solution to ((x-4)^2)/9+((y+2)^2)/(25)=1 is Ellipse with (h,k)=(4,-2),a=3,b=5