Question

If CF is perpendicular from the center C of the ellipse  on the tangent at any point P, and G is the point where the normal at P meets the minor axis, then (CF. PG)2 is equal to

Solution

Correct option is

2401

Equation of the tangent at  on the ellipse is

Then   

                      

Equation of the normal at P is

                      

Coordinates of G are 

            

                        

So (CF. PG)2 = (49)2 = 2401.

SIMILAR QUESTIONS

Q1

 

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

Q2

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

Q3

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

Q4

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

Q5

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

  

Q6

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

Q7

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

Q8

The point of intersection of the perpendicular tangents to the ellipse  lies on a circle square of whose radius is

 

Q9

If x + y = k is a normal to the parabola y2 = 12xp is the length of the perpendicular from the focus of the parabola on this normal; then 3k2 + 2p2 is equal to

Q10

If the length of the semi major axis of an ellipse is 68 and the eccentricity is  then the area of the rectangle formed by joining the vertices of the latera of the ellipse is equal to