weird parabola
Geometry
Level
pending
A line M through A is drawn parallel to BD. Point S moves such that its distance from the line BD and the vertex A are equal. If locus of S cuts at points X, Y, Z then area of triangle XYZ, is ?
1sq. unit
10 sq. unit
34 sq. unit
2 sq. unit
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1 solution
Consider a parabola having focus at A, let its axis meet its directrix at point G. Draw line parallel to directrix , (surely it would be the latus ractum) let the latus rectum cut parabola at points Y and Z. Let the parabola cut its axis at X . AG=/sqrt{2}., AX=XG=/sqrt{2}^{-1} Also , YZ us latus rectum So, YZ=4 /sqrt{2}^{-1} So, area of XYZ = 0.5 /sqrt{2}^{-1} 4 /sqrt{2}^{-1}=1