Question

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

Solution

Correct option is

2223

For the parabola y2 = 12x, equation of a normal will slope –1, is

              y = – x – 2(3)( –1) – (3)( –1)3           [m = –1, a = 3]

     x + y = 9  so  k = 9

Focus of the parabola is (3, 0)

    3k2 + 2p2 = 2223.

SIMILAR QUESTIONS

Q1

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

Q2

 

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

Q3

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

Q4

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

Q5

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

Q6

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

  

Q7

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

Q8

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

Q9

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

 

Q10

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