Question

If the line x – 1 = 0 is the directrix of the parabola y– ky + 8 = 0, then one of the of the value of k is

  

Solution

Correct option is

4

Parabola is 

or Y2 = 4AX, where 4A = kY = y

Its diretrix is X = – A or   

or    

Comparing with = 1, we get   

or  k2 + 4k – 32 = 0

     (k + 8)(k – 4) = 0      

k = – 8 is also true but it is not given in any of the four choices.

SIMILAR QUESTIONS

Q1

If normal at the point (at2, 2at) in the parabola y2 = 4axintersects the parabola again at the (am2, 2am), then find the minimum value of m2.

Q2

The equation of circle touching the parabola y2 = 4x at the point  (1, –2) and passing through origin is

Q3

The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is

Q4

Slope of common tangent to parabolas y2 = 4x and x2 = 8y is

Q5

If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12+ 34 = 0, then m is

Q6

If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is

Q7

PQ is a focal chord of the parabola y2 = 4axO is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.

Q8

Find the shortest distance between the circle x2 + y2 – 24y + 128 = 0 and the parabola y2 = 4x.

Q9

The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is  

Q10

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :