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. Letalpha, 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))alphabeta=0has its roots real and distinct.

Answer»


Solution :Clearly BK is a FOCAL chord so `alpha+beta+alphabeta RARR alpha beta=(100)/(9)`
For real and distinct roots `D gt 0`
`rArr""a^(2)gt 5a gt 14 lt0""rArr""gt 2 LT 7`
NUMBER of intergral values of a are 8.


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