The locus of intersection of locus of $P$ with $x + y = 2$
Step-by-Step Solution
Key Concept: A plane parallel to the $z$-axis with variable $x,y$ coordinates defines a conic section in that plane; when derived from equidistant foci, this is a hyperbola.
When a plane is parallel to the $z$-axis, the locus of points equidistant from two fixed points (foci) that lie on a line parallel to the $z$-axis forms a hyperbola. The plane cuts through the directrix surfaces in such a way that the ratio of distances satisfies the defining property of a hyperbola.
Correct Answer: I need to analyze this problem carefully. The question asks for the locus of intersection of locus of P with the line x + y = 2.
However, the question statement appears incomplete - it doesnt clearly define what the locus of P is. Based on the step-by-step solution provided, it mentions:
- Points equidistant from two fixed