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Find the point on the curve y=¼x2+1 which are nearest to the point (0,6). Answer--(±2√3,4)
Hi Shaleen,
Let (x,y) be any point on the curve.
To minimise the distance D = √[(x-6)^2 + y^2]
ie minimise (x-6)^2 + y^2.
Now y = x^2/4 + 1
So substitute for y, and you will get a function in x, say f(x).
For maxima or minima f[dash](x) = 0.
So solve for x from that equation, and you would get two values of x = ±2√3.
for this x value f[double dash](x) > 0, so minima point.
For these x, values of y from y = x^2/4 + 1 = 2.
Hence you get the point on the curve.
Hope that helps.
Best Regards,
Ashwin (IIT Madras).
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