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} + 5 y^{2} + 6 x - 40 y - 167 = 0

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

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

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

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

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)