Question

The sum of the squares of the perpendicular on any tangent to the ellipse  from two points on the minor axis, each at a distance  from the centre is 

Solution

Correct option is

2a2

 

Let e be the eccentricity of the ellipse. Then,   

    .     

Thus, two points on the minor axis are 

       

The equation of any tangent to the given ellipse is  

   

Now,  

   p1 = Length of the ⊥ from P(0, ae) on (i)   

           

and, 

   p2 = Length of the ⊥ from Q(0, –ae) on (i)      

       

  

  

 

SIMILAR QUESTIONS

Q1

Consider the family of circle x2 + y2 = r2, 2 < r < 5. If in the first quadrant the common tangent to a circle of the family and the ellipse 4x2 + 25y2 = 100 meets the coordinate axes at A and B, then find the equation of the locus of the mid point of AB.

Q2

The orbit of earth is an ellipse with eccentricity 1/60 with the sun at one focus the major axis being approximately 186 × 106 miles in length. Find the shortest and longest distance of the earth from the sun.   

Q3

 

A straight line PQ touches the ellipse  and the circle x2 + y2 = r(b < r < a). RS is a focal chord of the ellipse. If RSis parallel to PQ and meets the circle at points R and S. Find the length of RS

Q4

If α and β are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is 

Q5

, then the chord joining two points θ1 and θ2 on the ellipse  will subtend a right angle at

Q6

The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is a/an

Q7

The number of values of c such that the straight line y = 4x + ctouches the curve , is  

Q8

, then PF1 + PF2 equals

Q9

An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an

Q10

The eccentric angle of a point on the ellipse  whose distance from the centre of the ellipse is 2, is