Question

Consider the two curves C1 : y2 = 4xC2 : x2 + y2 – 6x + 1 = 0. Then,

Solution

Correct option is

C1 and C touch each other exactly at two points

Four points of intersection of circle and parabola, put y2 = 4x in the equation of the circle, we get x2 + 4x – 6x + 1 = 0 or  (x – 1)2 = 0 i.e., they intersect at two coincident points given by

     x = 1 and hence from parabola y2 = 4

  y = 2, –2.

Hence the two curves cut at two coincident points P(1, 2) and

Q(1, –2). Thus they touch at the above two points.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

  

Q4

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) :

Q5

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

Q6

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

Q7

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Q8

If  and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then

   

Q9

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid-point of PQ is

Q10

Angle between tangents drawn from the point (1, 4) to the parabola y2 = 4is