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If the line passing through the focus `S` of the parabola `y=a x^2+b x+c` meets the parabola at `Pa n dQ` and if `S P=4` and `S Q=6` , then find the value of `adot`

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Verified by Experts

The correct Answer is:
`pm(5)/(48)`
The length of latus rectum of`y=ax^(2)+bx+c" is "1//|a|`. Now, the semi-latus rectum is the HM of SP and SQ.
Then, we have
`(1)/(SP)+(1)/(SQ)=(2)/(1//|2a|)`
`or4|a|=(1)/(4)+(1)/(6)=(5)/(12)`
`ora=pm(5)/(48)`
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