Question

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

Solution

Correct option is

Rectangular hyperbola

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

   x – y = at                                  ….. (2)

(1)                       ….. (3)

Multiple (2) and (3),

       

⇒ Rectangular hyperbola

SIMILAR QUESTIONS

Q1

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 =

Q2

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

Q3

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

Q4

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

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

Q8

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

Q9

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

Q10

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