What is 7x^2+3y^2-42x+6y-39=0 ?

The solution to 7x^2+3y^2-42x+6y-39=0 is Ellipse with (h,k)=(3,-1),a=sqrt(15),b=sqrt(35)

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7x^2+3y^2-42x+6y-39=0

7 x^{2} + 3 y^{2} - 42 x + 6 y - 39 = 0

(h, k) = (3, - 1), a = 15, b = 35

Solution steps

7 x^{2} + 3 y^{2} - 42 x + 6 y - 39 = 0

Rewrite

7 x^{2} + 3 y^{2} - 42 x + 6 y - 39 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 15 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( 35 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 15, b = 35

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), b = 35, a = 15

3 x^{2} + 5 y^{2} = 8

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

\frac{( x - 3 ) ^{2}}{225} + \frac{( y + 9 ) ^{2}}{121} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{45} = 1

100 x^{2} + 4 y^{2} = 1

What is 7x^2+3y^2-42x+6y-39=0 ?
The solution to 7x^2+3y^2-42x+6y-39=0 is Ellipse with (h,k)=(3,-1),a=sqrt(15),b=sqrt(35)