What is 17x^2+10y^2+102x+80y+143=0 ?

The solution to 17x^2+10y^2+102x+80y+143=0 is Ellipse with (h,k)=(-3,-4),a=sqrt(10),b=sqrt(17)

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17x^2+10y^2+102x+80y+143=0

17 x^{2} + 10 y^{2} + 102 x + 80 y + 143 = 0

(h, k) = (- 3, - 4), a = 10, b = 17

Solution steps

17 x^{2} + 10 y^{2} + 102 x + 80 y + 143 = 0

Rewrite

17 x^{2} + 10 y^{2} + 102 x + 80 y + 143 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 10 ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( 17 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 4), a = 10, b = 17

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 4), b = 17, a = 10

(6 p + 5 q) 2 = 36 p^{2} + 25 q^{2}

3 x^{2} + 54 x + 243 + 2 y^{2} - 6 = 0

4 x^{2} + 9 y^{2} - 24 x + 36 y - 72 = 0

0.04 = 0.01 x^{2} + 0.04 y^{2}

3 x^{2} + 2 y^{2} \geq 18

What is 17x^2+10y^2+102x+80y+143=0 ?
The solution to 17x^2+10y^2+102x+80y+143=0 is Ellipse with (h,k)=(-3,-4),a=sqrt(10),b=sqrt(17)