ExamBro
ExamBro
TS EAMCET · Maths · Parabola

The normal at a point on the parabola \(y^2=4 x\) passes through \((5,0)\). If there are two more normals to this parabola which pass through \((5,0)\), the centroid of the triangle formed by the feet of these three normals is

  1. A \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
  2. B \((4,0)\)
  3. C \((0,2)\)
  4. D \((2,0)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((2,0)\)

Step-by-step Solution

Detailed explanation

We have, \(y^2=4 x \quad \therefore \quad a=1\) We know that, the centroid of the triangle formed by the conormal points on a parabola lies on its axis and its coordinates are \(\left(\frac{2}{3}(h-2 a), 0\right)\) where \((h, k)\) is the point through which all normals passes.…