What is (8x^2-12x+8y^2+20y+17)/8-2=0 ?

The solution to (8x^2-12x+8y^2+20y+17)/8-2=0 is Ellipse with (h,k)=(3/4 ,-5/4),a=sqrt(2),b=sqrt(2)

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(8x^2-12x+8y^2+20y+17)/8-2=0

\frac{8 x ^{2} - 12 x + 8 y ^{2} + 20 y + 17}{8} - 2 = 0

(h, k) = (\frac{3}{4}, - \frac{5}{4}), a = 2, b = 2

Solution steps

\frac{8 x ^{2} - 12 x + 8 y ^{2} + 20 y + 17}{8} - 2 = 0

Rewrite

\frac{8 x ^{2} - 12 x + 8 y ^{2} + 20 y + 17}{8} - 2 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{4} ) ^{2}}{( 2 ) ^{2}} + \frac{( y - ( - \frac{5}{4} ) ) ^{2}}{( 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{4}, - \frac{5}{4}), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{4}, - \frac{5}{4}), b = 2, a = 2

\frac{x ^{2}}{20} + \frac{y ^{2}}{25} = 1

16 x^{2} + 25 y^{2} - 32 x - 100 y - 284 = 0

9 x^{2} - 54 x + 4 y^{2} - 8 y - 59 = 0

\frac{( x + 5 ) ^{2}}{20} + \frac{( y - 6 ) ^{2}}{11} = 1

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

What is (8x^2-12x+8y^2+20y+17)/8-2=0 ?
The solution to (8x^2-12x+8y^2+20y+17)/8-2=0 is Ellipse with (h,k)=(3/4 ,-5/4),a=sqrt(2),b=sqrt(2)