What is ((x+3)^2)/(49)+((y+2)^2)/(21)=1 ?

The solution to ((x+3)^2)/(49)+((y+2)^2)/(21)=1 is Ellipse with (h,k)=(-3,-2),a=7,b=sqrt(21)

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((x+3)^2)/(49)+((y+2)^2)/(21)=1

\frac{( x + 3 ) ^{2}}{49} + \frac{( y + 2 ) ^{2}}{21} = 1

(h, k) = (- 3, - 2), a = 7, b = 21

Solution steps

\frac{( x + 3 ) ^{2}}{49} + \frac{( y + 2 ) ^{2}}{21} = 1

Rewrite

\frac{( x + 3 ) ^{2}}{49} + \frac{( y + 2 ) ^{2}}{21} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{7 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( 21 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 2), a = 7, b = 21

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 2), a = 7, b = 21

3 x^{2} + 2 y^{2} - 16 x + 15 = 0

\frac{x ^{2}}{400} + \frac{y ^{2}}{100} = 1

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

\frac{( x - 3 ) ^{2}}{7} + \frac{y ^{2}}{15} = 1

x^{2} - 6 x + 4 y^{2} + 16 y + 21 = 0

What is ((x+3)^2)/(49)+((y+2)^2)/(21)=1 ?
The solution to ((x+3)^2)/(49)+((y+2)^2)/(21)=1 is Ellipse with (h,k)=(-3,-2),a=7,b=sqrt(21)