What is 7x^2+16y^2+28x-128y+172=0 ?

The solution to 7x^2+16y^2+28x-128y+172=0 is Ellipse with (h,k)=(-2,4),a=4,b=sqrt(7)

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7x^2+16y^2+28x-128y+172=0

7 x^{2} + 16 y^{2} + 28 x - 128 y + 172 = 0

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

Solution steps

7 x^{2} + 16 y^{2} + 28 x - 128 y + 172 = 0

Rewrite

7 x^{2} + 16 y^{2} + 28 x - 128 y + 172 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x + 2 ) ^{2}}{16} + \frac{y ^{2}}{49} = 1

9 x^{2} + 36 x + y^{2} + 2 y + 36 = 0

4 y^{2} + x^{2} = 8

\frac{x ^{2}}{3} + \frac{y ^{2}}{5} = 1

25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0

What is 7x^2+16y^2+28x-128y+172=0 ?
The solution to 7x^2+16y^2+28x-128y+172=0 is Ellipse with (h,k)=(-2,4),a=4,b=sqrt(7)