Home
Class 12
MATHS
An equation of the elliptical part of an...

An equation of the elliptical part of an optical lens system is `(x^(2))/(25)+(y^(2))/(9)=1`. The parabolic part of the system has a focus in common with right focus of the ellipse. The vertex of the parabola is at the orgin and the prabola opens to the right. Find the equation of the parabola.

Text Solution

Verified by Experts

The correct Answer is:
16x
Promotional Banner

Topper's Solved these Questions

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY - II

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 5.1|14 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY - II

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 5.2|28 Videos

  • THEORY OF EQUATIONS

    PREMIERS PUBLISHERS|Exercise Problems for practice (Answer the following)|21 Videos

Similar Questions

Explore conceptually related problems

An equation of the elliptical part of an optical lens system is (x^(2))/(16)+(y^(2))/(9)=1 . The parabolic part of the system has a focus in common with the right focus of the ellipse. The vertex of the parabola is at the origin and the parabola opens to the right. determine the equation of the parabola

For the parabola y^2 = 8x , write its focus and the equation of the directrix.

If the vertex of the parabola is (3,2) and directrix is 3x+4y-(19)/7=0 , then find the focus of the parabola.

If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

If incident from point (-1,2) parallel to the axis of the parabola y^2=4x strike the parabola, then find the equation of the reflected ray.

Find the equation of parabola whose focus is (0,1) and the directrix is x+2=0. Also find the vertex of the parabola.

The parametric equation of a parabola is x=t^2+1,y=2t+1. Then find the equation of the directrix.

Show that the locus of a point that divides a chord of slope 2 of the parabola y^2=4x internally in the ratio 1:2 is parabola. Find the vertex of this parabola.

PREMIERS PUBLISHERS-TWO DIMENSIONAL ANALYTICAL GEOMETRY - II -PROBLEMS FOR PRACTICE
  1. An equation of the elliptical part of an optical lens system is (x^(2)...

    Text Solution

    |

  2. The point of intersection of the tangent at 't(1)' and 't(2)' to the ...

    Text Solution

    |

  3. The latus rectum of the parabola y^(2)-4x+4y+8=0 is:

    Text Solution

    |

  4. The point of contact of the tangent 2x+3y+9=0 to the parabola y^(2)=8x...

    Text Solution

    |

  5. The eccentricity of the ellipse 9x^(2)+5y^(2)-54x-40y+116=0 is:

    Text Solution

    |

  6. The area of the directrix circle of the ellipse (x^(2))/(16)+(y^(2))/(...

    Text Solution

    |

  7. If the length of the latus rectum is half the length of the conjucate ...

    Text Solution

    |

  8. The locus of the point of intersection of perpendicular tangents to th...

    Text Solution

    |

  9. The equation of the tangent to the parabola y^(2)=16x inclined at 60^(...

    Text Solution

    |

  10. The equation of conic with focus (-2,1) and directrix 3x-y+2=0 is:

    Text Solution

    |

  11. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 has the points A and B a...

    Text Solution

    |

  12. The point of contact of the line 2x-y+2=0 with the parabola y^(2)=16x ...

    Text Solution

    |

  13. The radius of the director circle of the hyperbola (x^(2))/(25)-(y^(2)...

    Text Solution

    |

  14. If 4x+y+k=0 is a tangent to the ellipse x^(2)+3y^(2)=3 then k = ?

    Text Solution

    |

  15. The tangent to the hyperbola 3x^(2)-y^(2)=3 parallel to 2x-y+4=0 is:

    Text Solution

    |

  16. The eccentricity of the ellipse for which the distance between the dir...

    Text Solution

    |

  17. The radius of the director circle of the hyperbola (x^(2))/(25)-(y^(2)...

    Text Solution

    |

  18. In are ellispe , the distance between its foci is 6 and its minor axi...

    Text Solution

    |

  19. The tangents at the points t(1) and t(2) on the parabola y^(2)=4ax are...

    Text Solution

    |

  20. The equation of normal at (-3,4) to the circle x^(2)+y^(2)=25 is 4x+3y...

    Text Solution

    |

  21. The equation of the ellipse with foci (pm2,0) vertices (pm3,0) is:

    Text Solution

    |