Home
Class 12
MATHS
A rectangle PQRS has its side PQ paralle...

A rectangle PQRS has its side PQ parallel to the line y= mx and vertices P,Q, and S on the lines y=a, x=b, and x=-b, respectively. Find the locus of the vertex R.

Text Solution

Verified by Experts

The correct Answer is:
`(m^(2)-1)x-my+b(m^(2)+1)+am=0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (Analytical and Descriptive Questions:)|4 Videos

  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (Match the column:)|1 Videos

  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Main Archive (State true or false: Q. 16 to 18)|3 Videos

  • SEQUENCE AND SERIES

    VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos

  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|34 Videos

Similar Questions

Explore conceptually related problems

A rectangle A B C D has its side A B parallel to line y=x , and vertices A ,Ba n dD lie on y=1,x=2, and x=-2, respectively. The locus of vertex C is x=5 (b) x-y=5 y=5 (d) x+y=5

A rhombus has two of its sides parallel to the lines y=2x+3 and y=7x+2 . If the diagonals cut at (1, 2) and one vertex is on the y-axis, find the possible values of the coordinate of that vertex.

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P (h, k) with the lines y = x and x + y = 2 is 4h^2 . Find the locus of the point P.

The sides of a rectangle are x and y, respectively. Find the rule for finding the perimeter of the rectangle.

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

The base of a triangle passes through a fixed point (f,g) and its sides are respectively bisected at right angles by the lines y+x=0 and y - 9x = 0 Determine the locus of its vertex.

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

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.

Let a line x/a+y/b=1 intersects the x-axis at A and y-axis at B resapectively. A line parallel to it is drawn to intersect the axes in P and Q respectively. The extermities of the lines are joined transversely. If the locus of point of intersection of the line joining them is x/a=cy/b, then c is equal to

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio

VMC MODULES ENGLISH-STRAIGHT LINES-JEE Advanced Archive
  1. about to only mathematics

    Text Solution

    |

  2. For points P-=(x1, y1) and Q-=(x2, y2) of the coordinate plane, a new ...

    Text Solution

    |

  3. A rectangle PQRS has its side PQ parallel to the line y= mx and vertic...

    Text Solution

    |

  4. A line through A(-5,-4) meets the lines x+3y+2=0,2x+y+4=0a n dx-y-5=0 ...

    Text Solution

    |

  5. If (alpha,alpha^2) lies inside the triangle formed by the lines 2x+3y-...

    Text Solution

    |

  6. Find the equation of the line passing through the point (2, 3) and ...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. A line cuts the x-axis at A (7, 0) and the y-axis at B(0, - 5) A varia...

    Text Solution

    |

  9. Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E...

    Text Solution

    |

  10. The equations of perpendicular bisectors o the sides AB and AC of a ...

    Text Solution

    |

  11. One diameter of the circle circumscribing the rectangle ABCD is 4y=x+7...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. The vertices of a triangle are [at(1)t(2),a(t(1)+t(2))],[at(2)t(3),a...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of...

    Text Solution

    |

  18. One side of a rectangle lies along the line 4x+7y+5=0. Two of its vert...

    Text Solution

    |

  19. For a point P in the plane, let d1(P)a n dd2(P) be the distances of th...

    Text Solution

    |

  20. A ray of light along x+sqrt(3) y = sqrt(3) gets reflected upon reachin...

    Text Solution

    |