Question

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

Solution

Correct option is

(x2 + y2)= 16x2 – 9y2

 

9x2 – 16y= 144  ⇒ Equation of tangent to hyperbola is

                                            …… (1)

                         …… (2)

Let (x1y1) be mid-point of the chord of circle x2 + y= 16 equation of this is

                 x x1 + y y1  (x12 + y12) = 0                        …… (3)

so 

eliminate m to get locus of (x1y1) as

    (x2 + y2)= 16x2 – 9y2

SIMILAR QUESTIONS

Q1

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

Q2

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.

Q3

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

Q4

 

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

.

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

The angle between lines joining origin to the points of intersection of the line  and the curve y2 – x2 = 4 is