Trig/Math

Find all the points having an x coordinate of 2 whose distance from the point (-1,-5) is 5.

so far i have
5=sqrt((-1-2)^2+(-2-y)^2)
5=(-3)^2

how do i simplify the rest of the equation so i can find x. do i foil it out? thanks.

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asked by Josh
  1. Geometrically, you are looking for the intersection of a vertical line (x=2) with a circle centred at (-1,-5) with a radius of 5.

    Line L1: x=2
    Circle C1: (x-(-1))²+(y-(-5))²=5²
    (x+1)²+(y+5)²=25
    Substitute x=2 in C1:
    (2+1)²+(y+5)²=25
    (y+5)²=25-3²=16=4²
    (y+5) = ±4
    So there are two solutions, y=-9 or y=-1

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  2. thank you!!

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    posted by Josh
  3. You're welcome.
    Do give a check on the distance between the centre and the intersection points to complete the question.

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