Question

Let P and , where , be two points on the hyperbola . If (h, k) is the point of intersection of the normal’s at P and Q, then k is equal to

Solution

Correct option is

 

P are two points on

                                                                     …… (1)

                                                                        …… (2)

Normal at P is   

                   

                     ……. (3)

Similarly normal at Q is

                            ……. (4)

To solve (3) and (4) for y multiplying (3) by sin Ï• and (4) by    sin θ, and then subtracting,

.

⇒ – by  = (a2 + b2) or y = k

 

SIMILAR QUESTIONS

Q1

Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola

4x2 – 9y2 =36.

Q2

Find the distance from A(4, 2) to the points in which the line 3x – 5= 2 meets the hyperbola xy = 24. Are these points on the same side of A?

Q3

The asymptotes of the hyperbola  makes an angle 600 with x-axis. Write down the equation of determiner conjugate to the diameter y = 2x.

Q4

Two straight lines pass through the fixed points  and have gradients whose product is k > 0. Show that the locus of the points of intersection of the lines is a hyperbola.

Q5

Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x2 – 3y2 = 6.

Q6

 

Find the range of ‘a’ for which two perpendicular tangents can be drawn to the hyperbola from any point outside the hyperbola

.

Q7

Find the hyperbola whose asymptotes are 2x – y = 3 and 3x + y – 7 = 0 and which passes through the point (1, 1).

Q8

The locus of a variable point whose distance from (–2, 0) is  times its distance from the line , is

Q9

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Q10

If x = 9 is the chord of contact of the hyperbola x2 – y= 9, then equation of corresponding of tangents is