What is (x+5)^2+3/10 y^2=34 ?

The solution to (x+5)^2+3/10 y^2=34 is Ellipse with (h,k)=(-5,0),a=sqrt(34),b=(2sqrt(85))/(sqrt(3))

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(x+5)^2+3/10 y^2=34

(x + 5)^{2} + \frac{3}{10} y^{2} = 34

(h, k) = (- 5, 0), a = 34, b = \frac{2 85}{3}

Solution steps

(x + 5)^{2} + \frac{3}{10} y^{2} = 34

Rewrite

(x + 5)^{2} + \frac{3}{10} y^{2} = 34

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 34 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2 85}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 0), a = 34, b = \frac{2 85}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 5, 0), b = \frac{2 85}{3}, a = 34

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

x^{2} + 4 y^{2} - x + 2 y = 8

6 x^{2} + 7 y^{2} = 6

- 4 y^{2} - 6 y = x^{2}

7 x^{(2)} + 10 y^{(2)} - 56 x + 100 y + 292 = 0

What is (x+5)^2+3/10 y^2=34 ?
The solution to (x+5)^2+3/10 y^2=34 is Ellipse with (h,k)=(-5,0),a=sqrt(34),b=(2sqrt(85))/(sqrt(3))