Question

A ray emanating from the point (5, 0) is incident on the hyperbola 9x2 – 16y2 = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lies in first quadrant.  

Solution

Correct option is

 

Given hyperbola is 9x2 – 16y2 = 144. This equation can be rewritten as                                                 

         

Since x coordinates of P is 8. Let y coordinate of P is α. 

  

  

    

  

Hence coordinates of point P is 

∵ Equation of reflected ray passing through     

∴ Its equation is  

        

  

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SIMILAR QUESTIONS

Q1

The foci of a hyperbola coincide with the foci of the ellipse . Find the equation of the hyperbola if its eccentricity is 2.

Q2

For what value of λ does the line y = 2x + λ touches the hyperbola  

Q3

Find the equation of the tangent to the hyperbola x2 – 4y2 = 36 which is perpendicular to the line x – y + 4 = 0.  

Q4

 

Find the equation and the length of the common tangents to hyperbola 

            

Q5

Find the locus of the foot of perpendicular from the centre upon any normal to the hyperbola .

Q6

Find the locus of the mid-points of the chords of the hyperbola  which subtend a right angle at the origin.

Q7

Find the locus of the poles of normal chords of the hyperbola 

Q8

Find the condition for the lines Ax2 + 2Hxy + By2 = 0 to be conjugate diameters of  .

Q9

Find the asymptotes of the hyperbola xy – 3y – 2x = 0.

Q10

The equations of the transverse and conjugate axes of a hyperbola are respectively 3x + 4y – 7 = 0, 4x – 3y + 8 = 0 and their respective lengths are 4 and 6. Find the equation of the hyperbola.