Question

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

Solution

Correct option is

9x2  8y– 18x + 9 =  0

 

= 9 is equation of chord of contact of

               x2– y2  = 0                                                           …… (1)

(x1y1) be the point of which  x = 9 is chord of contact

w.r.t curve (2) then x x1 – y y1 = 0

            

pair of tangents through (x1y1) = (1, 0) is T2 = SS1

                9x2 – 8y2 +18– 9 =  0

SIMILAR QUESTIONS

Q1

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?

Q2

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

Q3

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.

Q4

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

Q5

 

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

.

Q6

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

Q7

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

Q8

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

Q9

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

Q10

The locus of the mid-point of the chord of the circle x2 + y= 16, which are tangent to the hyperbola 9x2 – 16y= 144 is