Parabola
Normals
Grade 11
Question:
<p>Normals of parabola \(y^2 = 4x\) at P and Q meet at \(R(x_2, 0)\) and tangent at P and Q meet at \(T(x_1, 0)\). 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: Three distinct normals exist from a point on the axis only when the point lies beyond a critical distance from the vertex.
<p>For three distinct normals to be drawn from point R(\(x_2\), 0) to the parabola \(y^2 = 4x\), the condition is that R must satisfy certain inequalities. The possible value is \(x_2 = 8\).</p>
Correct Answer: r