What is 4x^2+y^2+40x+6y+95=0 ?

The solution to 4x^2+y^2+40x+6y+95=0 is Ellipse with (h,k)=(-5,-3),a=sqrt(7/2),b=sqrt(14)

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4x^2+y^2+40x+6y+95=0

4 x^{2} + y^{2} + 40 x + 6 y + 95 = 0

(h, k) = (- 5, - 3), a = \frac{7}{2}, b = 14

Solution steps

4 x^{2} + y^{2} + 40 x + 6 y + 95 = 0

Rewrite

4 x^{2} + y^{2} + 40 x + 6 y + 95 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( \frac{7}{2} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 14 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 3), a = \frac{7}{2}, b = 14

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 3), b = 14, a = \frac{7}{2}

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{25} = 1

3 x^{2} + 4 y^{2} - 16 x + 16 = 0

x^{2} + 2 y^{2} + 4 x + 2 y - 27 = 0

What is 4x^2+y^2+40x+6y+95=0 ?
The solution to 4x^2+y^2+40x+6y+95=0 is Ellipse with (h,k)=(-5,-3),a=sqrt(7/2),b=sqrt(14)