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From a point (sin k,cos k),three normal can be drawn to the parabola y^2=4ax(a>0) then then value of a lies in the interval:1)(2,5/2)2)(0,1/2)3)(2,3)4)(1/2,3/2)
Write the equation of normal and satisfy at this point .You will get conditions on the value such that three real roots must exist .Use h>2a condition for real roots.
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