Home
Class 12
MATHS
If P be a point on the parabola y^2=3(2x...

If P be a point on the parabola `y^2=3(2x-3)` and M is the foot of perpendicular drawn from the point P on the directrix of the parabola, then find length of each sides of an equilateral triangle SMP(where S is the focus of the parabola).

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|14 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|24 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|25 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

M is the foot of the perpendicular from a point P on a parabola y^2=4a x to its directrix and S P M is an equilateral triangle, where S is the focus. Then find S P .

M is the foot of the perpendicular from a point P on a parabola y^2=4a x to its directrix and S P M is an equilateral triangle, where S is the focus. Then find S P .

Foot of the directrix of the parabola y^(2) = 4ax is the point

A point on a parabola y^2=4a x , the foot of the perpendicular from it upon the directrix, and the focus are the vertices of an equilateral triangle. The focal distance of the point is equal to a/2 (b) a (c) 2a (d) 4a

If Q is the foot of the perpendicular from a point p on the parabola y^(2)=8(x-3) to its directrix. S is an equilateral triangle then find the lengh of side of the triangle.

A point P on the parabola y^(2)=4x , the foot of the perpendicular from it upon the directrix and the focus are the vertices of an equilateral triangle. If the area of the equilateral triangle is beta sq. units, then the value of beta^(2) is

Let x+y=k be a normal to the parabola y^(2)=12x . If p is the length of the perpendicular from the focus of the parabola onto this normal then 4k-2 p^(2) =?

The locus of foot of the perpendiculars drawn from the focus on a variable tangent to the parabola y^2 = 4ax is

If a point P on y^2x , the foot of the perpendicular from P on the directrix and the focus form an equilateral traingle , then the coordinates of P may be

A point P on the parabola y^2=12x . A foot of perpendicular from point P is drawn to the axis of parabola is point N. A line passing through mid-point of PN is drawn parallel to the axis interescts the parabola at point Q. The y intercept of the line NQ is 4. Then-

ARIHANT MATHS ENGLISH-PARABOLA-Exercise (Single Option Correct Type Questions)
  1. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  2. The normal to the parabola y^(2)=4ax at three points P,Q and R meet at...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. The largest value of a for which the circle x^2+y^2=a^2 falls totally ...

    Text Solution

    |

  5. From a point (sintheta,costheta), if three normals can be drawn to the...

    Text Solution

    |

  6. If two different tangents of y^2=4x are the normals to x^2=4b y , then...

    Text Solution

    |

  7. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

    Text Solution

    |

  8. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

    Text Solution

    |

  9. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

    Text Solution

    |

  10. An equilateral triangle SAB is inscribed in the parabola y^(2)=4ax hav...

    Text Solution

    |

  11. C is the center of the circle with center (0, 1) and radius unity. P i...

    Text Solution

    |

  12. Let S be the focus of y^2=4x and a point P be moving on the curve such...

    Text Solution

    |

  13. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

    Text Solution

    |

  14. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  15. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

    Text Solution

    |

  16. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |

  17. If the fourth term in the expansion of (a x+1/x)i s5/2,\ then find th...

    Text Solution

    |

  18. The set of points on the axis of the parabola y^2-4x-2y+5=0 find the s...

    Text Solution

    |

  19. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |

  20. if y=4x+3 is parallel to a tangent to the parabola y^2=12x, then its d...

    Text Solution

    |