Home
Class 11
MATHS
If the line l x+m y+n=0 touches the circ...

If the line `l x+m y+n=0` touches the circle `x^2+y^2=a^2` , then prove that `(l^2+m^2)a^2=n^2dot`

Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    RD SHARMA ENGLISH|Exercise All Questions|216 Videos

  • THE STRAIGHT LINES

    RD SHARMA ENGLISH|Exercise All Questions|493 Videos

Similar Questions

Explore conceptually related problems

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

If straight line lx + my + n=0 is a tangent of the ellipse x^2/a^2+y^2/b^2 = 1, then prove that a^2 l^2+ b^2 m^2 = n^2.

Prove that the line lx+my+n=0 toches the circle (x-a)^(2)+(y-b)^(2)=r^(2) if (al+bm+n)^(2)=r^(2)(l^(2)+m^(2))

The line l x+m y+n=0 is a normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . then prove that (a^2)/(l^2)+(b^2)/(m^2)=((a^2-b^2)^2)/(n^2)

A line L is perpendicular to the line 3x-4y-7=0 and touches the circle x^(2)+y^(2)-2x-4y-4=0 , the y -intercept of the line L can be:

A line L is perpendicular to the line 3x-4y-7=0 and touches the circle x^(2)+y^(2)-2x-4y-4=0 , the y -intercept of the line L can be:

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0

RD SHARMA ENGLISH-THE CIRCLE-All Questions
  1. If 2x^2+lambdax y^+2y^2+(lambda-4)x+6y-5=0, is the equation of a circ...

    Text Solution

    |

  2. If the equation of a circle is lambdax^2+(2lambda-3)y^2-4x+6y-1=0, th...

    Text Solution

    |

  3. If the line l x+m y+n=0 touches the circle x^2+y^2=a^2 , then prove th...

    Text Solution

    |

  4. Find the equation of the circle which passes through the origin and...

    Text Solution

    |

  5. Prove that the locus of a point which moves such that the sum of th...

    Text Solution

    |

  6. <img src="https://d10lpgp6xz60nq.cloudfront.net/physicsimages/BMSDPP01...

    Text Solution

    |

  7. A dip circle is at right angles to the magnetic meridian. What w...

    Text Solution

    |

  8. Find the equation to the circle which passes through the points (1,2...

    Text Solution

    |

  9. Find the equation of the circle, the coordinates of the end points ...

    Text Solution

    |

  10. If the circles x^2+y^2+2a x+c=0a n dx^2+y^2+2b y+c=0 touch each other,...

    Text Solution

    |

  11. Find the equation of the circle which passes through the points (1,-2)...

    Text Solution

    |

  12. The equation of the circle which touches the axes of coordinates an...

    Text Solution

    |

  13. Find the equation of the circle which passes through the points (2,...

    Text Solution

    |

  14. The number of integral values of lambda for which the equation x^2+y^2...

    Text Solution

    |

  15. Find the equation of the circle which touches the lines 4x-3y+10=0a...

    Text Solution

    |

  16. If the line y=sqrt(3)x+k touches the circle x^2+y^2=16 , then find t...

    Text Solution

    |

  17. Find the equation of the circle having (1,-2) as its centre and passi...

    Text Solution

    |

  18. Find the locus of the centre of the circle touching the line x+2y=0...

    Text Solution

    |

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

    Text Solution

    |

  20. Find the equation of the circle which touches x-axis and whose centre ...

    Text Solution

    |