Question

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

Solution

Correct option is

Let the coordinates of P be (), then PQ = 2β

Since P () also lie on hyperbola

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

Portion of asymptote of hyperbola  (between center and the tangent at vertex) in the first quadrant is cut by the line

+ λ (x – a) = 0 (λ is a parameter) then

Q8

If a variable line , which is a chord of the hyperbola  (b > a), subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is

Q9

If values of m for which the line  touches the hyperbola 16x2 – 9y= 144 are the roots of the equation 

x2 – (a + b)x – 4 = 0, then value of (a, b) is equal to

Q10

Let any double ordinate PNP’ of the hyperbola  be produced both sides to meet the asymptotes in Q and Q’, then PQP’Q is equal to