Thread: eqn of circle and tangent
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Old July 3rd, 2009, 06:55 AM
Tesla23 Tesla23 is offline
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Quote:
Originally Posted by helloying View Post
find the eqn of the circle that passes through the point A(8,1) and B(7,1) and has , for its tangent at B, the line 3x-4y-21=0
centre of circle must lie on perp bisector of AB which is line x = 7.5, so let centre be C be the point (7.5,y)

so we need to find y such that |AC| = distance of C to line 3x-4y-21=0 so:

(7.5 - 7)^2 + (y - 1)^2 = \frac{(3*7.5 - 4y - 21)^2}{3^2 + 4^2}

which you can solve for y

Edit: I missed the "Tangent at B" part of the question, and as pointed out by HallsOfIvy the line 3x-4y-21=0 does not pass through B, this solution finds the circle passing through A and B with tangent 3x-4y-21=0
Last edited by Tesla23; July 3rd, 2009 at 07:28 AM.
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