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The tangent PT and the normal PN to the ...

The tangent PT and the normal PN to the parabola `y^2=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 `((2a)/3,0)`

B

directrix is at x=0

C

latusrectum is `(2a)/3`

D

focus is (a,0)

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The correct Answer is:
A, D
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ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
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  4. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

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  7. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

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  8. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

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  9. The shortest distance between line y-x=1 and curve x=y^2 is

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  10. Let S be the focus of the parabola y^2=8x and let PQ be the common cho...

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  11. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

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  12. Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the ...

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  13. The slope of the line touching the parabolas y^2=4x and x^2=-32y is

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  14. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

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  15. Let a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, ...

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  16. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

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  17. Let O be the vertex and Q be any point on the parabola,x^2=""8y . I...

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  18. ·If the normals of the parabola y^2=4x drawn at the end points of it...

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  19. Let the curve C be the mirror image of the parabola y^2 = 4x with resp...

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  20. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

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