What is 3x^2+5y^2+6x-10y+7=0 ?

The solution to 3x^2+5y^2+6x-10y+7=0 is Ellipse with (h,k)=(-1,1),a=sqrt(1/3),b=sqrt(1/5)

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3x^2+5y^2+6x-10y+7=0

3 x^{2} + 5 y^{2} + 6 x - 10 y + 7 = 0

(h, k) = (- 1, 1), a = \frac{1}{3}, b = \frac{1}{5}

Solution steps

3 x^{2} + 5 y^{2} + 6 x - 10 y + 7 = 0

Rewrite

3 x^{2} + 5 y^{2} + 6 x - 10 y + 7 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = \frac{1}{3}, b = \frac{1}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), a = \frac{1}{3}, b = \frac{1}{5}

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

4 x^{2} + y^{2} - 16 x + 8 y - 20 = 0

x^{2} - 4 x + 16 y^{2} + 32 y + 4 = 0

9 x^{2} + 12 y^{2} = 108

x^{2} + 3 y^{2} + 4 x + 18 y + 22 = 0

What is 3x^2+5y^2+6x-10y+7=0 ?
The solution to 3x^2+5y^2+6x-10y+7=0 is Ellipse with (h,k)=(-1,1),a=sqrt(1/3),b=sqrt(1/5)