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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

16 - x^{2} - 9 y^{2} \geq 0

9 x^{2} + 6 y^{2} + 54 x - 36 y + 81 = 0

36 x^{2} + 25 y^{2} - 900 = 0

- 8 x^{2} - 2 y^{2} - 12 = 0

(x - 2)^{2} + \frac{( y + 3 ) ^{2}}{16} = 1

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