Home
Class 12
MATHS
If the foot of the perpendicular from th...

If the foot of the perpendicular from the origin to a straight line is at `(3,-4)` , then find the equation of the line.

Text Solution

Verified by Experts

The correct Answer is:
3x-4y=25
Let P(3,-4) be the foot of the perpendicular from the origin O on the required line. Then the slope of OP is
`(-4-0)/(3-0) = -(4)/(3)`
Therefore, the slope of the required line is 3/4.
Hence, its equation is
`y+4 = (3)/(4)(x-3)`
or 3x-4y = 25
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.2|4 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.3|7 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

The coordinate of the foot of the perpendicular drawn from the origin to a plane are (12, -4, 3). Find the equation of the plane.

The perpendicular from the origin to a line meets it at the pooint (-2, 9),find the equation of the line.

The perpendicular from the origin to a line meets it at the point (-2,9) find the equation of the line.

If the foot of the perpendicular from the origin to a plane is (2,-3,4), then the equation of the plane is

The foot of the perpendicular drawn from the origin to a plane is (2, -3, -4). Find the equation of the plane.

The locus of the foot of the perpendicular from the origin to a straight line passing through (1,1) is

The foot of perpendicular drawn from the origin to the plane is (4,-2,-5). Find the equation of the plane.

The foot of the perpendicular drawn from the origin to a plane is (1,2,-3). Find the equation of the plane.or If O is the origin and the coordinates of P is (1,2,-3), then find the equation of the plane passing through P and perpendicular to OP.

The coordinates of the foot of a perpendicular drawn from the origin to the plane are (2, 3, 1). Find the equation of the plane in vector form.

The perpendicular from the origin to a line L meets it at the point (3, -9) , equation of the line L is

CENGAGE-STRAIGHT LINES-Exercise 2.1
  1. Find the equation of the line perpendicular to the line x/a-y/b=1 and ...

    Text Solution

    |

  2. If the middle points of the sides B C ,C A , and A B of triangle A B C...

    Text Solution

    |

  3. Find the equations of the lines which pass through the origin and are ...

    Text Solution

    |

  4. If (-2,6) is the image of the point (4,2) with respect to line L=0, th...

    Text Solution

    |

  5. Find the area bounded by the curves x+2|y|=1 and x=0 .

    Text Solution

    |

  6. Find the equation of the straight line passing through the intersectio...

    Text Solution

    |

  7. If the foot of the perpendicular from the origin to a straight line is...

    Text Solution

    |

  8. A straight line through the point (2,2) intersects the lines sqrt(3)x+...

    Text Solution

    |

  9. The equation of the straight line passing through the point (4. 3) and...

    Text Solution

    |

  10. A straight line through the point A(3, 4) is such that its intercept ...

    Text Solution

    |

  11. A straight line L is perpendicular to the line 5x-y=1 . The area of th...

    Text Solution

    |

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

    Text Solution

    |

  13. A line L1-=3y-2x-6=0 is rotated about its point of intersection with t...

    Text Solution

    |

  14. The diagonals A C and B D of a rhombus intersect at (5,6)dot If A-=(3,...

    Text Solution

    |

  15. Find the equation of the straight line which passes through the origin...

    Text Solution

    |

  16. A line intersects the straight lines 5x-y-4=0 and 3x-4y-4=0 at A and B...

    Text Solution

    |

  17. In the given figure, PQR is an equilateral triangle and OSPT is a squa...

    Text Solution

    |

  18. Two fixed points A and B are taken on the coordinates axes such that O...

    Text Solution

    |

  19. A regular polygon has two of its consecutive diagonals as the lines sq...

    Text Solution

    |

  20. Find the direction in which a straight line must be drawn through the...

    Text Solution

    |