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A (-2,0) and B(2, 0) are two fixed points and P is a point such that PA-PB=2. Let S be the circle x^(2)+y^(2)=r^(2). Then match the following lists: |
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Answer» <P>  The locus of point P satisfying `PA-PB=2` is a BRANCH of the HYPERBOLA `x^(2)-y^(2)//3=1`. For r = 2, the circle and the branch of the hyperbola INTERSECT at two points. For r = 1, there is one point of intersection. If m is the SLOPE of the common tangent, then `m^(2)-3=r^(2)(1+m^(2))` `"or"x^(2)=(r^(2)+3)/(1-r^(2))` Hence, there are no common tangents for r gt 1 and two common tangents for r lt 1. |
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