Question

Given the parabola whose equation is x^2=1/5y, find the focus and determine if the parabola opens up or down.

Answer 1

coefficient of x^2 is positive so it opens upwards.

Answer 2

Focus of Parabola is ( 0 , 0.05 ) and it opens in upward direction.

Explanation:

Given Equation of Parabola :
`x^2=(1)/(5)y`

We have to find focus of Parabola and direction in which it opens.

Since Given equation of parabola is quadratic in x. and positive focus so it opens in Positive direction of y-axis that is in upward direction.

Now to find focus we compare it with stand equation of parabola.

x² = 4ax

where ( 0 , a ) is focus

So,
`4a=(1)/(5)`

`a=(1)/(20)=0.05`

Therefore, Focus of Parabola is ( 0 , 0.05 ) and it opens in upward direction.