Home
Class 12
MATHS
Consider the points A(0,1)a n dB(2,0),a ...

Consider the points `A(0,1)a n dB(2,0),a n dP` be a point on the line `4x+3y+9=0` . The coordinates of `P` such that `|P A-P B|` is maximum are (a) `(-(24)/5,(17)/5)` (b) `(-(84)/5,(13)/5)` (c) `((31)/7,(31)/7)` (d) `(-3,0)`

Text Solution

Verified by Experts

The correct Answer is:
B

The equation of AB is
`y-1 = (0-1)/(2-1)x or x+2y-2=0`
`|PA-PB| le AB`
Thus, |PA-PB| is maximum if the points A,B, and P are collinear.
Hence, solving x+2y-2=0 and 4x+3y+9=0, we get point `P-=(-24//5, 17//5).`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWERS TYPE)|30 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (LINKED COMPREHENSION TYPE)|27 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.6|5 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Consider the point A(3,4) and B(7,13).If P be a point on the line y=x, the co-ordinate of point P if PA+PB is minimum.

Consider the point A(3,4)and B(7,13).If be a point on the line y=x,such that |PA+PB| is minimum, then co-ordinate of P is

The coordinates of the point P on the lines 2x+3y+1=0, such that |PA-PB| is maximum, where A is (2,0) and B is (0,2) is

Consider the points A(0, 0, 0), B(5, 0, 0), C(3, 0, 4) and D(0, 4, 3). The line AC and BD are-

Consider the points A(0, 0, 0), B(5, 0, 0), C(3, 0, 4) and D(0, 4, 3). The points A, B, C and D are-

Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such that x y >0a n dx+y<1, then P

Let P be a point on the circle x^2+y^2=9,Q a point on the line 7x+y+3=0 , and the perpendicular bisector of P Q be the line x-y+1=0 . Then the coordinates of P are (a) (0,-3) (b) (0,3) ((72)/(25),(21)/(35)) (d) (-(72)/(25),(21)/(25))

The line 9x+y-18=0 is the chord of contact of the point P(h , k) with respect to the circle 2x^2+2y^2-3x+5y-7=0 , for (a) ((24)/5,-4/5) (b) P(3,1) (c) P(-3,1) (d) (-2/5,(12)/5)

The area of triangle A B C is 20c m^2dot The coordinates of vertex A are (-5,0) and those of B are (3,0)dot The vertex C lies on the line x-y=2 . The coordinates of C are (a) (5,3) (b) (-3,-5) (-5,-7) (d) (7,5)

Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that P Q+Q R+R P is minimum. Then the coordinates of Q are ((17)/4,0) (b) (17 ,0) ((17)/2,0) (d) none of these

CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (SINGLE CORRECT ANSWER TYPE)
  1. The range of values of theta in the interval (0, pi) such that the poi...

    Text Solution

    |

  2. Distance of origin from the line (1+sqrt3)y+(1-sqrt3)x=10 along the li...

    Text Solution

    |

  3. Consider the points A(0,1)a n dB(2,0),a n dP be a point on the line 4x...

    Text Solution

    |

  4. Consider the point A(3,4) and B(7,13).If P be a point on the line y=x,...

    Text Solution

    |

  5. The area enclosed by 2|x|+3|y|lt=6 is (a) 3 sq. units (b) 4 sq. uni...

    Text Solution

    |

  6. A B C is a variable triangle such that A is (1, 2), and Ba n dC on the...

    Text Solution

    |

  7. In A B C , the coordinates of the vertex A are (4,-1) , and lines x-y...

    Text Solution

    |

  8. P is a point on the line y+2x=1, and Qa n dR two points on the line 3y...

    Text Solution

    |

  9. If the equation of base of an equilateral triangle is 2x-y=1 and the v...

    Text Solution

    |

  10. The locus of a point that is equidistant from the lines x+y - 2sqrt2 =...

    Text Solution

    |

  11. If the quadrilateral formed by the lines ax + by + c = 0, a'x + b'y + ...

    Text Solution

    |

  12. A line of fixed length 2 units moves so that its ends are on the pos...

    Text Solution

    |

  13. If the extremities of the base of an isosceles triangle are the points...

    Text Solution

    |

  14. A-=(-4,0),B-=(4,0)dotMa n dN are the variable points of the y-axis s...

    Text Solution

    |

  15. The number of triangles that the four lines y = x + 3, y = 2x + 3, y =...

    Text Solution

    |

  16. A variable line x/a + y/b = 1 moves in such a way that the harmonic me...

    Text Solution

    |

  17. Given A (0, 0) and B (x,y)with x epsilon (0,1) and y>0. Let the slope ...

    Text Solution

    |

  18. A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n ...

    Text Solution

    |

  19. Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that ...

    Text Solution

    |

  20. If a pair of perpendicular straight lines drawn through the origin f...

    Text Solution

    |