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
- A \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
- B \((4,0)\)
- C \((0,2)\)
- D \((2,0)\)
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.…
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