The Locus Of The Foot Of The Perpendicular Drawn From The Centre Of The Ellipse  on Any Tangent Is 

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Question

The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is 

Solution

Correct option is

 

Let P(hk) be the foot of the perpendicular drawn from the centre C(0, 0) of the ellipse to any tangent  

         

Then, 

        

Since CP is perpendicular to the tangent given in (i). 

  

Substituting the value of m in (ii), we get 

       

Hence, the locus of P(hk) is  

      .

Testing

SIMILAR QUESTIONS

Q1

Let S(3, 4) and S(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent to the ellipse is (1, –4), then the eccentricity of the ellipse is 

Q2

Let S and S’ be two foci of the ellipse . If a circle described on SS’ as diameter intersects the ellipse in real and distinct points, then the eccentricity e of the ellipse satisfies   

Q3

If PSQ is a focal chord of the ellipse , then the harmonic mean of SP and SQ is  

Q4

If PSQ is a focal chord of the ellipse 16x2 + 25y2 = 400 such that SP = 8, then SQ =

Q5

If S and S’ are two focii of the ellipse 16x2 + 25y2 = 400 andPSQ is a focal chord such that SP = 16, then SQ = 

Q6

Tangent at a point on the ellipse  is drawn which cuts the coordinates axes at A and B. The minimum area of the triangleOAB is (O being origin)

Q7

The locus of the foot of the perpendicular from the foci on any tangent to the ellipse 

Q8

The locus of the point of intersection of tangents to the ellipse  at the points whose eccentric angles differ by  is  

Q9

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is 

Q10

, be the end points of the latusrectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latusrectum PQ are