Optimizing a Focal Line

★ 8/10Completing the Square conic sections analytic geometry inequality Vieta's Formulas

Problem

The line $\ell: x = my + c$ ( $c > 0$ ) meets the parabola $y^2 = 4x$ at $A, B$ . Let $P$ be the intersection of the parabola's directrix with the $x$ -axis. The area of $\triangle PAB$ equals $4c + 4$ . When $2m + c$ is maximal, find the equation of $\ell$ .

Answer

Solution

Difficulty	8/10
Topics	Completing the Square, conic sections, analytic geometry, inequality, Vieta's Formulas

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.