Home
Class 12
MATHS
If the line 3x-4y-lambda=0 touches the ...

If the line `3x-4y-lambda=0` touches the circle `x^2 + y^2-4x-8y- 5=0` at (a, b) then which of the following is not the possible value of `lambda+a + b`?

A

20

B

`-28`

C

`-30`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Line `3x - 4y -lambda =0` touches the circle.
`rArr lambda = 15, -35`
For `lambda = 15`, point of contact `(a,b)` is `(5,0)`
For `lambda = - 35`, point of contact `(a,b)` is `(-1,8)`.
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    CENGAGE|Exercise Multiple Correct Answers Type|9 Videos

  • CIRCLES

    CENGAGE|Exercise Comprehension Type|8 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

Similar Questions

Explore conceptually related problems

The lines joining the origin to the point of intersection of 3x^2+m x y-4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3

If the line k^(2)(x-1)+k(y-2)+1=0 touches the parabola y^(2)-4x-4y+8=0 , then k can be

If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

The acute angle between the line 3x-4y=5 and the circle x^2+y^2-4x+2y-4=0 is theta . Then 9costheta=

Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x^2-9y^2 +30 = 0 (b) 4x^2-9y^2-30 = 0 (c) 9x^2-4y^2-30=0 (d) none of these

Find the centre and radius of circles. x^(2)+y^(2)-4x-8y-45=0 .

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

If the lines 3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0 and 2x - 3y +lambda = 0 are concurrent, then the value of lambda is

CENGAGE-CIRCLES-Question Bank
  1. If the line 3x-4y-lambda=0 touches the circle x^2 + y^2-4x-8y- 5=0 a...

    Text Solution

    |

  2. If a x+b y=10 is the chord of minimum length of the circle (x-10)^2+(y...

    Text Solution

    |

  3. Locus of the poirit of intersection of the pair of perpendicular tange...

    Text Solution

    |

  4. Let A B and C D are two parallel chords of circle whose radius is 5 un...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. A straight line l1 with equation x-2y+10=0 meets the circle with equat...

    Text Solution

    |

  7. If the tangent at the point P on the circle x^2+y^2+6 x+6 y=2 meets th...

    Text Solution

    |

  8. The radius of the circle whose two normals are represented by the equa...

    Text Solution

    |

  9. If the diagram, D C is a diameter of the large circle centered at A, a...

    Text Solution

    |

  10. If 2 x-3 y=0 is the equation of the common chord of the circles, x^2+y...

    Text Solution

    |

  11. If one of the diameters of the circle x^2+y^2-2 x-6 y+6 =0 is a chord ...

    Text Solution

    |

  12. A circle touches the y-axis at the point (0, 4) and cuts the x-axis in...

    Text Solution

    |

  13. In the figure given, two circles with centres Ct and C2 are 35 units a...

    Text Solution

    |

  14. If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle, then fi...

    Text Solution

    |

  15. The maximum distance of the point (4,4) from the circle x^2+y^2-2 x-...

    Text Solution

    |

  16. If the circle (x-a)^2+y^2=25 intersects the circle x^2+(y-b)^2=16 in s...

    Text Solution

    |

  17. If a circle S(x, y)=0 touches at the point (2,3) of the line x+y=5 and...

    Text Solution

    |