Question

The locus of the middle point of the chords of hyperbola 3x2 – 2y2 + 4x – 6y = 0 parallel to y = 2x is

Solution

Correct option is

3x – 4y = 4

 

Given  3x2 – 2y2 + 4x – 6y = 0                           …… (1)

             y = 2x                                                    …… (2)

let (x1y1) be mid-point of chord of (1)

⇒ equation is

     (3x+ 2)x + (2y1 – 3)y1 + (2x1 – 3y1) = 3x12  2y12 + 4x1 – 6y1

Now slope  locus is 3x – 4y = 4

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

If a circle cuts a rectangular hyperbola xy = c2 in A, B, C, D and the parameters of these four points be t1t2t3 and t4 respectively. Then

Q9

The equation of the conic with focus at (1, –1), directrix along – y + 1 = 0 and with eccentricity  is

Q10

The angle between the asymptotes of the hyperbola  is