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1.题目在直角坐标系xOy中,曲线C:y=x~2/4与直线l:y=kx+a(a>0)交于M、N两点.(1)当k=0时,分别求C在点M和N处的切线方程;(2)y轴上是否存在点P,使得当k变动时,总有∠OPM=∠OPN?说明理由.(2015年全国Ⅰ卷)
1. Problem In the Cartesian coordinate system xOy, the curve C: y = x ~ 2/4 and the line l: y = kx + a (a> 0) intersect at M and N. (1) When k = 0 , Find the tangent equation of C at points M and N, respectively; (2) Is there any point P on the y-axis so that there is always ∠OPM = ∠OPN?