Home
Class 11
MATHS
Points A, B, C lie on the parabola y^2=4...

Points A, B, C lie on the parabola `y^2=4ax` The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the `triangle ABC` and `triangle PQR`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The tangents to the parabola y^2=4ax at P(at_1^2,2at_1) , and Q(at_2^2,2at_2) , intersect at R. Prove that the area of the triangle PQR is 1/2a^2(t_1-t_2)^3

In two similar triangles A B C and P Q R , if their corresponding altitudes A D and P S are in the ratio 4:9, find the ratio of the areas of triangle A B C and triangle P Q R .

Prove that the tangents drawn on the parabola y^(2)=4ax at points x = a intersect at right angle.

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

Let A, B, C be three points on the parabola y^(2)=4ax such that tangents at these points taken in pairs form a triangle PQR. Then, area (DeltaABC) : (Delta PQR) =

A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ is:

From a variable point R on the line y = 2x + 3 tangents are drawn to the parabola y^(2)=4ax touch it at P and Q point. Find the locus of the centroid of the triangle PQR.

From a point (h,k) three normals are drawn to the parabola y^2=4ax . Tangents are drawn to the parabola at the of the normals to form a triangle. The Centroid of G of triangle is

The tangent at the point P(x_1, y_1) to the parabola y^2 = 4 a x meets the parabola y^2 = 4 a (x + b) at Q and R. the coordinates of the mid-point of QR are

The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equation of the normal to curve x^2=4y which passes throug...

    Text Solution

    |

  2. Show that the locus of a point that divides a chord of slope 2 of the ...

    Text Solution

    |

  3. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

    Text Solution

    |

  4. If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k ...

    Text Solution

    |

  5. Let P be a point whose coordinates differ by unity and the point does ...

    Text Solution

    |

  6. Statement 1: The line x-y-5=0 cannot be normal to the parabola (5x-15)...

    Text Solution

    |

  7. If (h ,k) is a point on the axis of the parabola 2(x-1)^2+2(y-1)^2=(x+...

    Text Solution

    |

  8. Column I, Column II Points from which perpendicular tangents can...

    Text Solution

    |

  9. Consider the parabola y^2=12 x Column I, Column II Equation of ta...

    Text Solution

    |

  10. If the tangent at the point P(2,4) to the parabola y^2=8x meets the pa...

    Text Solution

    |

  11. Let P be the family of parabolas y=x^2+p x+q ,(q!=0), whose graphs cut...

    Text Solution

    |

  12. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

    Text Solution

    |

  13. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

    Text Solution

    |

  14. The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with...

    Text Solution

    |

  15. Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .Tangent...

    Text Solution

    |

  16. The equation of the directrix of the parabola with vertex at the origi...

    Text Solution

    |

  17. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

  18. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

    Text Solution

    |

  19. Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 to...

    Text Solution

    |

  20. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

    Text Solution

    |