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

x^{2} - 16 x + 4 y^{2} - 12 y + 16 = 0

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

\frac{y ^{2}}{b ^{2}} = 1 - \frac{x ^{2}}{a ^{2}}

- 1 (- 4 x^{2} - y^{2} + 16) \geq - 1 (0)

\frac{x ^{2}}{14} + \frac{y ^{2}}{8} = 1

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)