1.

For a parabolay^(2)-2y-4x+9=0 the tangent at some point B is 3y=x+10, where the normal at some other point K is 27y-9x+10=0. Let alpha and betaare the segments of the chord BK cut by the axes of the parabola. Find the number of integral values of ‘a’ for which the equation3x^(2)-(alpha+beta)x+(a^(2)-5a+ (353)/(27)) alpha beta=0 has its roots real and distinct

Answer»


Solution :Clearly BK is a FOCAL chord so`alpha+ beta= alpha beta rArr alpha, beta =(100)/(9)`
For real and distinct ROOTS
`rArr a^(2)-5a-14 lt 0 rArr -2 lt a lt 7`
number of INTEGRAL values of a are 8


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