4. Proof: The point of intersection of the two curves is p^2*1/x+x=2p which is (x-p)^2=0. It can be seen that there is only one point of intersection at x=p for the two curves. Therefore, it can be concluded that the equation of the tangent is p^2*y+x=2p.
If the equation of the tangent is 9y+x=-6, then p=-3 which is the point asked.
5. Solution:
Let the tangent line be y=ax+B. Then ax+B=6*x^0.5 from which it can be found that B=9/a and (36-2kB)/(2*k^2)=4. That is a=1.5 and B=6. Then A is easily found to be -6/1.5=-4. Then the distance AB is [6^2+(-4)^2]^0.5=52^0.5=2*13^0.5. Therefore, k=2.
才看到你还求翻译啊，你是在国外读书吗？回头再给你翻译吧。
If the equation of the tangent is 9y+x=-6, then p=-3 which is the point asked.
5. Solution:
Let the tangent line be y=ax+B. Then ax+B=6*x^0.5 from which it can be found that B=9/a and (36-2kB)/(2*k^2)=4. That is a=1.5 and B=6. Then A is easily found to be -6/1.5=-4. Then the distance AB is [6^2+(-4)^2]^0.5=52^0.5=2*13^0.5. Therefore, k=2.
才看到你还求翻译啊，你是在国外读书吗？回头再给你翻译吧。
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