Question

The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are

Solution

Correct option is

1, –1

Focus (a, 0) is (4, 0). Any focal chord is

           y – 0 = m(x – 4)

or       mx – y – 4m = 0.

Apply the condition of tangency p = t with circle (6, 0), .

          

or     2m2 = m2 + 1  m2 = 1

.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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.

Q6

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

Q7

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

Q8

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

  

Q9

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) :

Q10

The curve described parametrically by x = t2 + t + 1, y = t2 – + 1 represents.