Question

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

Solution

Correct option is

 

Let (hk) be the foot of the perpendicular drawn from the focusS(ae, 0) on tangent    

         

,    

       

  

Also, SP is perpendicular to (i)  

  

From (ii) and (iii), we get  

      

Hence, the locus of (hk) is x2 + y2 = a2

SIMILAR QUESTIONS

Q1

Tangents are drawn to the ellipse  and the circle x2 + y2 = a2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then, the greatest acute angle between these tangents is given by 

Q2

The area of the quadrilateral formed by the tangents at the end-points of latusrecta to the ellipse 

Q3

If α – β = constant, then the locus of the point of intersection of tangents at  to the ellipse   

Q4

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 

Q5

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   

Q6

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

Q7

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

Q8

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

Q9

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)

Q10

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