<p>Normals of parabola \(y^2 = 4x\) at P and Q meet at \(R(x_2, 0)\). The possible values of \(x_2\) so that 3 distinct normals can be drawn to the parabola from point R is/are</p>
Step-by-Step Solution
Key Concept: The number of normals from an external point depends on the cubic equation's discriminant.
<p>From a point \(R(h, 0)\) on the axis, the equation of normals to \(y^2 = 4x\) is:</p><p>\(y = m(x - h) - 2m - m^3\)</p><p>Substituting in parabola equation and solving for m gives a cubic in m.</p><p>For 3 distinct normals, this cubic must have 3 real roots. The condition is \(h \geq 2\).</p><p>At the boundary, three distinct normals exist when \(x_2 = 8\).</p>
Correct Answer: r