Question

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

Solution

Correct option is

Slope of the normal to the rectangular hyperbola xy = 4 is m = t2 = 2 and 2x – y = 5 has slope = 2.

         

Equation of the normal is 

⇒ ty – 2 = 2t (– 2t)

⇒ ty – 2 = 2tx – 4t2

⇒ 2tx – ty + 2 – 4t2 = 0

     

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

Five points are selected on a circle of radius a. the centers of the rectangular hyperbolas, each passing through four of these pints lie on a circle of a radius