 |
| ||
| |||
|
| Math Central | Quandaries & 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 |
Renson,
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?
Harley
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.