Question

If l is the length of the intercept made by a common tangent to the circle x2 + y= 16 and the ellipse , on the coordinate axes, then 81l2+ 3 is equal to

Solution

Correct option is

5295

Equation of any tangent to the ellipse is , which also touches the circle if

          

  

 and equation of the common tangent is

            

  

    

.

SIMILAR QUESTIONS

Q1

If the parabola C and D intersect at a point A on the line L1, then equation of the tangent point L at A to the parabola D is

Q2

If a > 0, the angle subtended by the chord AB at the vertex of the parabola is

Q3

P is a point on the circle C, the perpendicular PQ to the major axis of the ellipse E meets the ellipse at M, then  is equal to

Q4

Equation of the diameter of the ellipse conjugate to the diameter respected by L is 

Q5

 

If R is the point of intersection of the line L with the line x = 1, then 

Q6

If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of tangents is

Q7

If R is the point of intersection of the tangents to H at the extremities  of the chord L, then equation of the chord contact of with respect to the parabola P is

Q8

If the chord of contact of R with respect to the parabola Pmeets the parabola at T and T’, S is the focus of the parabola, then Area of the triangle STT’ is equal to

Q9

Tangent are drawn from any point on the hyperbola  to the circle x2 + y2 = 9. If the locus of the mid-point of the chord of contact is

  

Q10

If d is the length of the tangent from the point (100, 81) to the ellipse , then d2 is equal to