SOLUTION: Find a point (x,y) equidistant from point (-3,8) and the line 5x-4y+3=0

Question 1128771: Find a point (x,y) equidistant from point (-3,8) and the line 5x-4y+3=0
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find a point (x,y) equidistant from point (-3,8) and the line L1 5x-4y+3=0
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It's a parabola. The focus is (-3,8) and the directrix is 5x-4y+3 = 0
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For any point (x,y) the distance to (-3,8) is sqrt((x+3)^2 + (y-8)^2)
The distance from (-3,8) to the line L1 is |5x -4y +3|/sqrt(41) = 44/sqrt(41)
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Find the line perpendicular to L1 thru (-3,8), then the intersection of that line and L1.
Then find the midpoint from (-3,8) to the intersection.

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