Question

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

Solution

Correct option is

y = x + 2

Any tangent to y2 = 8x(a = 2) is . If it is a tangent to xy = –1, then it will cut the hyperbola in two coincident points.

     Δ = 0 i.e., 4 – 4m2 = 0   

Hence y = x + 2 is the common tangent.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

   

Q5

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

Q6

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

Q7

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

Q8

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

Q9

 

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

Q10

A tangent and a normal are drawn at the point P(16, 16) of the parabola y2 = 16x which cut the axis of the parabola at the points A and B respectively. If the center of the circle through P, A and B is C, then angle between PC and axis of x is