Question

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

Solution

Correct option is

2

Let the point be 

Chord of contact of hyperbola T = 0

               

  

Since this passes through point (x1y1)

∴  x1 = 2y1 and y1c + 1 = 0

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

A, B, C and D are the points of intersection of a circle and a rectangular hyperbola which have different centers. If AB passes through the center of the hyperbola, then CD passes through

Q9

Sa circle with fixed center (3h, 3k) and of variable radius cuts the rectangular hyperbola x2 – y2 = 9a2 at the points A, B, C, D. The locus of the centroid of the triangle ABC is given by

Q10

If PQ is a double ordinate of the hyperbola  such the OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies –