Question

 

The equation of the common tangent touching the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis is

Solution

Correct option is

 

Any tangent to the parabola y2 = 4x is

        

or    m2x – my + 1 = 0                         … (1)

Apply p = r the condition of tangency with given circle (3, 0), 3

       

or   3m2 = 1    

Since the tangent touches the parabola above x-axis it will make an acute angle with x-axis so that  = + ive.

Hence we choose . Put in (1)

 

SIMILAR QUESTIONS

Q1

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) :

Q2

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

Q3

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

Q4

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

Q5

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

   

Q6

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

Q7

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

Q8

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

Q9

The angle between the tangents drawn from the origin to the parabola y2 = 4a(x – a) is

Q10

The equation of the common tangent to the curves y2 = 8x and xy = –1 is