Given the parabola whose equation is y^2=-2/7x

Question

find the focus and determine if the parabola opens felt or right.?

 

 

Answer 1

Equation of parabola is y² = (-2/7)x.

Since there is a y² but no x², the parabola is horizontal and its equation is in the form     

x = a(y - k)² + h with vertex (h, k) and focus (h+1/(4a), k).

If a < 0, the parabola opens to the left.

If a > 0, the parabola opens to the right.

Rearrange the equation to solve for x.

y² = (-2/7)x

x = (-7/2)y²

The coefficient of y² is negative, so the parabola opens to the left.

vertex = (0, 0).

Therefore h+1/(4a) = 0+1/(4·-7/2) where h = 0 and a = -7/2

= 1÷(-4·7/2)

= -2/28

= -1/14

focus = (-1/14, 0)

Focus = (-1/14, 0) and the parabola opens to the left.