Question

The locus of the point of intersection of perpendicular tangents to.

Solution

Correct option is

 

Equation of any tangent to 

        

The equation of a tangent to  perpendicular to (i) is

      

  

Let P(hk) be the point of intersection of (i) and (ii). Then, 

                                                                            

  

  

Hence, the locus of (hk) is

      .

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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)

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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