Find the Focus of $$(2x+y-1)^2=5(x-2y-3)$$.
Clearly its a Parabola whose axis is $2x+y-1=0$ and since $x-2y-3=0$ is perpendicular to $2x+y-1=0$ Tangent at the vertex is $x-2y-3=0$.Also the Vertex is $(3,-1)$, but now how to find its focus?
2026-04-23 02:10:57.1776910257
Focus of the Parabola
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HINT:
Compare with $$Y^2=4aX$$ whose focus $(a,0)$