Math CentralQuandaries & Queries


Question from Renson, a student:

Determine whether the line x-2y=0 cuts,touches or fail to meet the circle x^2+y^2-8x+6y-15=0.If it touches or cuts ,find the coordinates of the point(s) of contact


If (x,y) is a point on the line then x = 2y. If (x,y) is on the circle then (x,y) also satisfies the equation of the circle. Thus you can substitute x = 2y in the equation

x2 + y2 - 8x + 6y - 15 = 0

to arrive at a quadratic in y which you can solve. For each y value find the corresponding x value using x = 2y.

How many intersection points did you find?


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