Parabola
Normals and tangents
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 \(T(x_1, 0)\). If \(x_2 = 3\), then area of quadrilateral PTQR is</p>
Step-by-Step Solution
Key Concept: Use the property that if normals at P and Q meet at R on axis, then area of quadrilateral depends on the x-coordinate of R.
<p>For \(x_2 = 3\) (where normals meet), using properties of parabola, the coordinates of P and Q can be found. The tangent intersection point \(x_1\) and the quadrilateral area can be calculated. Area of PTQR = \(3\sqrt{2}\).</p>
Correct Answer: p