The Equation Of The Line Of Latum Of The Rectangular Hyperbola xy = c2 is

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

The equation of the line of latum of the rectangular hyperbola xy = c2 is

Solution

Correct option is

OA = c                   A = (c, c)

AS = eOA         (∴  e = )

AS = 

       

Equation of line through LL’

Slope of line = –1and passing through   is

   

.

                                                                                

Testing

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is

Q8

A straight line intersects the same branch of the hyperbola  in P1 and P2 and meets its asymptotes in Q1 and Q2. Then P1Q2 – P2Q1 is equal to

Q9

From a point on the line y = x + c, c (parameter), tangents are drawn to the hyperbola  such that chords of contact pass through a fixed point (x1y1). Then  is equal to

Q10

If the portion of the asymptotes between center and the tangent at the vertex of hyperbola  in the third quadrant is cut by the line  being parameter, then