Question

The equation of the tangents to the conic 3x2 – y2 = 3 perpendicular to the line x + 3y = 2 is

Solution

Correct option is

     x + 3y = 2                                     ... (1)

Any line ⊥ to (1) is 

    3x – y + c = 0 ⇒ = 3x + c           … (2)

Now (2) tangent to hyperbola

 

    

SIMILAR QUESTIONS

Q1

The equation of the hyperbola referred to it axes as axes of coordinates whose latus rectum is 4 and eccentricity is 3, is

Q2

If a rectangular hyperbola whose center is C, is cut by any circle of radiusr in the four points P, Q, R, S, then 

CP2 + CQ2 + CR2 + CS2 =

Q3

If θ is the angle between the asymptotes of the hyperbola   with eccentricity e, then 

Q4

If the two lines x – a = 0 and y – b =  0 are conjugate w.r.t. the hyperbolaxy = c2, then the locus of (a, b) is

Q5

If P is a point on the hyperbola 16x– 9y2 = 144 whose foci are S1 andS2, then PS1 – PS2 =

Q6

The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is

Q7

The locus of the point of intersection of the lines (x + y)t = a and x – y = at, where t is the parameter, is 

Q8

If PQ is a double ordinate of the hyperbola  such that OPQ is an equilateral triangle, O being the center of the hyperbola. Then the eccentricity e of the hyperbola satisfies

Q9

A rectangular hyperbola passes through the points A(1, 1), B(1, 5), and C(3, 1). The equation of normal to the hyperbola at A(1, 1) is