Question

Regan is trying to find the equation of a quadratic that has a focus of (-2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand

Answer 1

If you have two points, \((x_1, y_1)\), the focus, and \((x_2, y_2)\) the directrix, both points can be inserted into the formula \((x - x_1)^2 + (y - y_2)^2 = (x - x_2)^2 + (y - y_2)^2\) and simplified to find the equation of the parabola.

1st Observation
The line y = 13 can be represented as the point (x, 13).

2nd Observation
From the 1st observation, you now have two points \((-2,5)\) and \((x, 13)\) which can be inserted into the given formula and simplified to arrive at the equation of the parabola.

Answer 2

Thank you!! one more question
Roy exclaims that his quadratic with a discriminant of -9 has no real solutions. Roy then puts down his pencil and refuses to do any more work. Create an equation with a negative discriminant. Then explain to Roy, in calm and complete sentences, how to find the solutions, even though they are not real.

Answer 3

It is best to work with one problem at a time. That is the way Open Study was designed.

Answer 4

how do i find X for the first problem?

Answer 5

You don't. You insert x into the formula in place of \(x_2\)