How to Find the Ordinate of P for Minimum AB in a Quadrant Curve?

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The discussion focuses on finding the ordinate of point P on the curve defined by the equation y = 7 - x², such that the line segment AB, formed by the intersections of the tangent at P with the coordinate axes, is minimized. The solution provided is that the ordinate of P, which minimizes AB, is 49/8. Participants emphasize the importance of showing prior attempts to facilitate better assistance in solving the problem.

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P is a point in the first quadrant on the curve: y = 7 - x2 . By P is drawn tangent to the curve, and A and B are points at which cut to the coordinate axes. Find the ordinate of P so that AB is minimum

Answer = 49/8
 
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What have you tried and where are you stuck? We do expect for people to show what they've tried so we have at least some idea where they are in the problem and how we can assist them to proceed...when you just post the problem, we have no idea how to best help you. :D
 
MarkFL said:
What have you tried and where are you stuck? We do expect for people to show what they've tried so we have at least some idea where they are in the problem and how we can assist them to proceed...when you just post the problem, we have no idea how to best help you. :D

ok If P (x0,y0)
the tangent must be yy0+xx0
the interception of the curve xith x axe is +/-sqrt7 and y = 7
I don't know how to assemble the equations
How can I proceed?
 
Last edited:

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