When No Point Exists

★ 7/10Circles analytic geometry Casework Apollonius Circle

Problem

In the coordinate plane, let $A(3, 0)$ and $B(0, t)$ with $t > 0$ . If there is no point $P$ in the plane simultaneously satisfying

|PA|^2 + 2|PO|^2 = 12 \qquad \text{and} \qquad |PO| = \sqrt{2}|PB|,

find the range of possible values of $t$ .

Answer

Solution

Difficulty	7/10
Topics	Circles, analytic geometry, Casework, Apollonius Circle

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.