The Locus Of The Point Of Intersection Of The Lines (x + Y)t = a and x – Y = At, Where t is The Parameter, 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.



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


Correct option is

Rectangular hyperbola

(x + y)t = a                                  ….. (1)

   x – y = at                                  ….. (2)

(1)                       ….. (3)

Multiple (2) and (3),


⇒ Rectangular hyperbola



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 =


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


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


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


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


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


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


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


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


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