Question

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

Solution

Correct option is

6

      The equation of the hyperbola differs from the equation of the asymptotes by a constant.

 The equation of the hyperbola with asymptotes 3x + y – 7 = 0   

     and 2x – y = 3 is

     (3x + y – 7)(2x – y – 3) + k = 0

It passes through (1, 1)  k = – 6

Hence the equation of the hyperbola is

      (3x + y – 7)(2x – y – 3) = 6

SIMILAR QUESTIONS

Q1

Let two perpendicular chords of the ellipse  each passing through exactly one of the foci meet at a point P. If from P two tangents are drawn to the hyperbola , then 

Q2

If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of triangle is.

Q3

Find the equations of tangents to the hyperbola x2 – 4y = 36 which are perpendicular to the line x – y + 4 = 0

Q4

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

4x2 – 9y2 =36.

Q5

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?

Q6

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

Q7

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.

Q8

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

Q9

 

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

.

Q10

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