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Consider two curves y^2 = 4a(x-lambda) and x^(2)=4a(y-lambda), where agt0 and lambda is a parameter. Show that (i) there is a single positive value of lambda for which the two curves have exactly one point of intersection in the 1st quadrant find it. (ii) there are infinitely many nagetive values of lambda for which the two curves have exactly one points of intersection in the 1st quadrant. (iii) if lambda=-a , then find the area of the bounded by the two curves and the axes in the 1st quadrant. |
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