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Math Help - Tangent to the Circle

  1. #1
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    Tangent to the Circle

    Hi there, stuck on a tangent question.

    a. Show that the point P(5,10) lies on the circle with equation (x+1)^2 + (y-2)^2 = 100.

    b. PQ is a diameter of this circle as shown in the diagram. Find the equation of the tangent at Q.

    I can do part a, and know how to find the equation of a tangent, but I don't know how to get the coordinates of Q so I can solve the equation.

    Thanks in advance
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  2. #2
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    Tangents to circles are always perpendicular to the circle's radius/diameter.
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  3. #3
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by HighlyFlammable View Post
    Hi there, stuck on a tangent question.

    a. Show that the point P(5,10) lies on the circle with equation (x+1)^2 + (y-2)^2 = 100.

    b. PQ is a diameter of this circle as shown in the diagram. Find the equation of the tangent at Q.

    I can do part a, and know how to find the equation of a tangent, but I don't know how to get the coordinates of Q so I can solve the equation.

    Thanks in advance
    if your query is "how to locate point Q" then do the following :
    1) call the centre of the circle as C. find the equation of line PC.
    2) take the intersections of the line PC with the circle given in the question. One of these will be Q.
    (can you see why this is so?)
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  4. #4
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    Hello highlyflammable,
    From the given circle equation id the center of the circle
    What is the slope of PO O the center
    What is the slope of the tangent at Q
    What are the coordinates of Q
    Use the point slope formula to find the equation
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