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Y2 = 4x is a parabola normals are drawn at point P and Q and R to meet at apoint (3,0) FINDcircumradius of tri.PQR Centroid of tr. PQRCircumcentre of PQR

Y2 = 4x is a parabola normals are drawn at point P and Q and R to meet at apoint (3,0) FINDcircumradius of tri.PQR Centroid of tr. PQRCircumcentre of PQR

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
equation of normal in slope form is given by
y= mx-2m-m^3
3,0 satisfies this eq, therefore m^3 – m =0
  • M=0,1,-1
Eq of the three normals is : y=0 ; y=x-3 ; y=3-x
Solving each with parabola we get two set of points : (0,0) (1,-2) (1,2)
And (0,0) (9,6) (9,-6)
These are the vertices of the triangle
Centroid =( 2/3,0) or (6,0)
Circumradius= ∆/s = 2/ (2/(√5+2))= √5+2.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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