The normal at a point on the parabola y^2=4x passes through (5,0). If two more normals to this parabola also pass through(5,0), then the centroid of…

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

MARKS Content Team · Accepted Answer

Correct answer: (B) (2,0). The given equation of a parabola, y^2=4x The equation of normal at a point P(5,0) y=-tx+2t+t^3 0=-5t+2t+t^3 3t=t^3 t^2=3 t=±√3,0 Here, a=1 Co-normal point Pat12,2at_1=(3,2√3) Qat22,2at_2=(3,-2√3) Rat32,2at_3=(0,0) The centroid is, C=(3+3+0)/3,(2√3-2√3+0)/3 C=6/3,0=2,0

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

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The normal at a point on the parabola y2=4x passes through (5,0). If two more normals to this parabola also pass through(5,0), then the centroid of the triangle formed by the feet of these three normals is

Solution

Relevant Questions

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