What is 10x^2+40x+7y^2+70y+145=0 ?

The solution to 10x^2+40x+7y^2+70y+145=0 is Ellipse with (h,k)=(-2,-5),a=sqrt(7),b=sqrt(10)

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10x^2+40x+7y^2+70y+145=0

10 x^{2} + 40 x + 7 y^{2} + 70 y + 145 = 0

(h, k) = (- 2, - 5), a = 7, b = 10

Solution steps

10 x^{2} + 40 x + 7 y^{2} + 70 y + 145 = 0

Rewrite

10 x^{2} + 40 x + 7 y^{2} + 70 y + 145 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( 7 ) ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( 10 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 5), a = 7, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 5), b = 10, a = 7

4 x^{2} + 4 y^{2} = 100 - 20 x + x^{2}

6 = x^{2} + 9 y^{2}

1 = \frac{( x - 3 ) ^{2}}{16} + \frac{y ^{2}}{4}

(3 x - 3)^{2} + (- 2 y - 4)^{2} = 43 + 9 + 16

36 x^{2} + 81 y^{2} = 49

What is 10x^2+40x+7y^2+70y+145=0 ?
The solution to 10x^2+40x+7y^2+70y+145=0 is Ellipse with (h,k)=(-2,-5),a=sqrt(7),b=sqrt(10)