## Question

### 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