Home
Class 12
MATHS
An equilateral triangle is inscribed wit...

An equilateral triangle is inscribed within the parabola `y^(2)=4ax` with one vertex at the chords of the parabola. Find the lenghtof side of triangle .

Text Solution

Verified by Experts

The correct Answer is:
`9 sqrt(3a)` unit
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise CALCULUS|84 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise ALGEBRA|141 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

An equilateral triangle is inscribed in the parabola y^(2)=4ax , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

An equilateral teiangle is inscribed in the parabola y^(2)=x whose one vertex is the vartex of the parabola. Then the length of a side of the triangle is-

An equilateral triangle is inscribed in the parabola y^2=4a x , such that one vertex of this triangle coincides with the vertex of the parabola. Then find the side length of this triangle.

An equilateral triangle inscribe a parabola y^2 = 4ax . such that oneof the vertex of the triangle lies on the vertex of the parabola-. Find the,length of,the each side. of the triangle:

The triangle P Q R of area A is inscribed in the parabola y^2=4a x such that the vertex P lies at the vertex of the parabola and the base Q R is a focal chord. The modulus of the difference of the ordinates of the points Qa n dR is

A right-angled triangle A B C is inscribed in parabola y^2=4x , where A is the vertex of the parabola and /_B A C=pi/2dot If A B=sqrt(5), then find the area of A B Cdot

The equation of one arm of a equilateral triangle is x + y = 2 and the co-ordinate of the vertex opposite to this arm is (2, -1). Find the length of one arm of this triangle.

P(alpha,alpha) is a point on the parabola y^(2)=4ax . Show that the normal chord of the parabola at P subtends a right angle at its focus.

Find the vertex of the parabola x^2=2(2x+y) .

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. If two distinct chords, drawn from the point (p,q) on the circle x^(2)...

    Text Solution

    |

  2. A variable line L passing through the point B(2,5) intesects the lines...

    Text Solution

    |

  3. For all values of a and, b show that the circle (x-2)(x-2+a)+(y+3) (y+...

    Text Solution

    |

  4. A circle C(1) of diameter 6 units, is in the first quadrant and it tou...

    Text Solution

    |

  5. Find he point on the straight line y=2x+11 which is nearest to the cir...

    Text Solution

    |

  6. On the parabola y^(2)=4ax, P is the point with parameter t,Q is the op...

    Text Solution

    |

  7. Through the vertex A of a parabola the chords AP and AQ are drawn at ...

    Text Solution

    |

  8. Show that the sum of the ordinate of end of any chord of a system of p...

    Text Solution

    |

  9. An equilateral triangle is inscribed within the parabola y^(2)=4ax wit...

    Text Solution

    |

  10. P,Q and R three points on the parabola y^(2)=4ax. If Pq passes through...

    Text Solution

    |

  11. A line of length (a+b) unit moves in such a way that its ends are alwa...

    Text Solution

    |

  12. show that the length of the focal chord of the ellipse (x^(2))/(a^(2))...

    Text Solution

    |

  13. A rod of given length (a+b) unit moves so that its ends are always on ...

    Text Solution

    |

  14. If theta and phi be the eccentric angles of the extremities of a focal...

    Text Solution

    |

  15. theta and phi are the eccentric angles of two points on an ellipse who...

    Text Solution

    |

  16. PQ and PR are two focal chords of the ellipse (x^(2))/(a^(2))+(y^(2))/...

    Text Solution

    |

  17. Find the locus of middle points of chords of the ellipse (x^(2))/(a^(2...

    Text Solution

    |

  18. Find the length of chord of the ellipse (x^(2))/(25)+(y^(2))/(16)=1, ...

    Text Solution

    |

  19. An ellipse has OB as a semi-minor axis, F and F' are its two foci and ...

    Text Solution

    |

  20. Let P b any point on the hyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 w...

    Text Solution

    |