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The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose
  • a)
    vertex is
  • b)
    directrix is x = 0
  • c)
    latus rectum is 2a/3
  • d)
    focus is (a, 0)
Correct answer is option 'A,D'. Can you explain this answer?
Most Upvoted Answer
The tangent PT and the normal PN to the parabola y2 = 4ax at a point ...
Equation of tangent and normal at point P(at2, 2at) is:
ty = x + at2 and y = −tx + 2at + at2
Let the centroid of △PTN be R(h, k).
∴ h =
And k = ⇒ 3h = 2a + a .
⇒ 3h = 2a +
⇒ 9k2 = 4a(3h − 2a)
Therefore, locus of centroid = y2 =
And vertex ; Directrix
Latus rectum = 4a/3
Therefore, focus
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Community Answer
The tangent PT and the normal PN to the parabola y2 = 4ax at a point ...
Equation of tangent and normal at point P(at2, 2at) is:
ty = x + at2 and y = −tx + 2at + at2
Let the centroid of △PTN be R(h, k).
∴ h =
And k = ⇒ 3h = 2a + a .
⇒ 3h = 2a +
⇒ 9k2 = 4a(3h − 2a)
Therefore, locus of centroid = y2 =
And vertex ; Directrix
Latus rectum = 4a/3
Therefore, focus
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The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whosea)vertex is b)directrix is x = 0c)latus rectum is 2a/3d)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer?
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The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whosea)vertex is b)directrix is x = 0c)latus rectum is 2a/3d)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whosea)vertex is b)directrix is x = 0c)latus rectum is 2a/3d)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whosea)vertex is b)directrix is x = 0c)latus rectum is 2a/3d)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer?.
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