Home
Class 11
MATHS
Let a given line L1 intersect the X and ...

Let a given line `L_1` intersect the X and Y axes at P and Q respectively. Let another line `L_2` perpendicular to `L_1` cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , 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 striaght line intersect x-axis at A(7,0) and y-axis at B(0,-5). The straight line PQ is perpendicular to AB and intersect the x and y-axes at P adn Q respectively. Find the eqution to the locus of the point of intersection of the line AQ and BP.

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

For the variable t , the locus of the points of intersection of lines x - 2y = t and x + 2y = (1)/(t) is _

Show that the circle with the portion of the line 3x + 4y = 12 intercepted between the axes as diameter passes through the origin.

Find the equation of the smallest circle passing through the point of intersection of the line x+y=1 and the circle x^(2)+y^(2)=9 .

Show that the circle with the portion of the line 3x + 4y = 12 intercepted between the axes as diameter, passes through the origin.

Show that the circle with the portion of the line 3x + 4y = 12 intercepted between the axes as diameter , passes through the origin .

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

If the straight line ax+y+6=0 passes through the point of intersection of the lines x+y+4=0 and 2x+3y+10=0 , find a.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The chords of contact of the pair of tangents drawn from each point on...

    Text Solution

    |

  2. The circle x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two ...

    Text Solution

    |

  3. Let a given line L1 intersect the X and Y axes at P and Q respectively...

    Text Solution

    |

  4. Lines 5x + 12y - 10 = 0 and 5x - 12y - 40 = 0 touch a circle C1 of dia...

    Text Solution

    |

  5. On the line segment joining (1, 0) and (3, 0) , an equilateral triangl...

    Text Solution

    |

  6. From a point R(5,8) , two tangents R Pa n dR Q are drawn to a given ci...

    Text Solution

    |

  7. Find the equations of the circles passing through the point (-4,3) and...

    Text Solution

    |

  8. Let A be the centre of the circle x^2+y^2-2x-4y-20=0 Suppose that the ...

    Text Solution

    |

  9. If r1and r2 are the radii of smallest and largest circles which passes...

    Text Solution

    |

  10. From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn...

    Text Solution

    |

  11. If C1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair o...

    Text Solution

    |

  12. The minimum radius of the circle which is orthogonal with both the c...

    Text Solution

    |

  13. If a circle of radius r is touching the lines x^2-4x y+y^2=0 in the ...

    Text Solution

    |

  14. Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a fa...

    Text Solution

    |

  15. Two circles of radii a and b touching each other externally, are inscr...

    Text Solution

    |

  16. Let C be any circle with centre (0,sqrt(2))dot Prove that at most two ...

    Text Solution

    |

  17. Let a circle be given by 2x(x-a)+y(2y-b)=0,(a!=0,b!=0) . Find the cond...

    Text Solution

    |

  18. Consider a family of circles passing through the points (3, 7) and (6,...

    Text Solution

    |

  19. Let xa n dy be real variables satisfying x^2+y^2+8x-10 y-40=0 . Let a=...

    Text Solution

    |

  20. A(1/(sqrt(2)),1/(sqrt(2))) is a point on the circle x^2+y^2=1 and B is...

    Text Solution

    |