Question:medium

If $P(\alpha,\alpha+1)$ is the foot of the perpendicular drawn from the origin to the line $L$ and the $x$-intercept of $L$ is \[ \left(-\frac52,0\right), \] then the sum of the squares of the distances from the origin to all such possible points $P$ is

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If $(x_1,y_1)$ is the foot of the perpendicular from the origin to a line, then the line can be written directly as \[ x_1x+y_1y=x_1^2+y_1^2. \] This avoids finding slopes and makes intercept conditions easy to apply.

Updated On: Jul 29, 2026

$\dfrac{45}{8}$
$\dfrac{15}{2}$
$\dfrac{12}{5}$
$\dfrac{10}{7}$

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The Correct Option is A

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If \(P(\alpha,\alpha+1)\) is the foot of the perpendicular drawn from the origin to the line \(L\) and the \(x\)-intercept of \(L\) is \[ \left(-\frac52,0\right), \] then the sum of the squares of the distances from the origin to all such possible points \(P\) is

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The Correct Option is A

Solution and Explanation

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