Home
Class 11
MATHS
Prove that the line through the point (x...

Prove that the line through the point `(x_1, y_1)`and parallel to the line `A x+B y+C=0`is `A(x-x_1)+B(y-y_1)=0`.

Text Solution

Verified by Experts

Given line Ax+By+C=0,
Slope of the given line is `-A div B`
Required line is passing through (x1 , y1)
`( y -y1) = (-A div B) times (x-x1)`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NCERT|Exercise MISCELLANEOUS EXERCISE|24 Videos

  • STRAIGHT LINES

    NCERT|Exercise EXERCISE 10.1|14 Videos

  • STRAIGHT LINES

    NCERT|Exercise SOLVED EXAMPLES|28 Videos

  • STATISTICS

    NCERT|Exercise EXERCISE 15.2|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise EXERCISE 3.1|7 Videos

Similar Questions

Explore conceptually related problems

Prove that the line through the point x_1 , y_1) and parallel to the line Ax+By+C=0 is A(x-x_1) + B (y-y_1)=0 .

Show that the equation of a line passing through a given point (x_(1),y_(1)) and perpendicular to the line ax+by +c =0 is b(x- x_(1))-a(y-y_(1)) =0.

Find the equation of a line passing through point (5, 1) and parallel to the line 7x – 2y + 5 = 0. (a)7x-2y-33=0 (b)6x-8y=0 (c)5x-8y-9=0 (d)None of these

The equation of the plane through the point (-1,2,0) and parallel to the lines (x)/(3)=(y+1)/(0)=(z-2)/(-1) and (x-1)/(1)=(y+1)/(2)=(2z+5)/(-1)

The equation of the plane thorugh the point (-1,2,0) and parallel to the lines x/3=(y+1)/0=(z-2)/(-1) and (x-1)/1=(2y+1)/2=(z+1)/(-1) is (A) 2x+3y+6z-4=0 (B) x-2y+3z+5=0 (C) x+y-3z+1=0 (D) x+y+3z-1=0

The equation of the plane through the point (-1,2,0) and parallel to the line (x)/(3)=(y+1)/(0)=(z-2)/(-1) and (x)/(3)=(2y+1)/(2)=(2z+1)/(-1) is

Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is

A straight line passes through the point (2,-1,-1). It is parallel to the plane 4x+y+z+2=0 and is perpendicular to the line (x)/(1)=(y)/(-2)=(z-5)/(1). The equation of the straight line is

The line 3x-2y=24 meets x-axis at A and y-axis at B. The perpendicular bisector of AB meets the line through (0, -1) and parallel to x-axis at C. Then C is: (A) (-7/2,-1) (B) (-15/2,-1) (C) (-11/2,-1) (D) (-13/2,-1)

A line through point A(1,3) and parallel to the line x-y+1 = 0 meets the line 2x-3y + 9 = 0 at point P. Find distance AP without finding point P.

NCERT-STRAIGHT LINES-EXERCISE 10.3
  1. The line through the points (h, 3) and (4, 1) intersects the line 7x-9...

    Text Solution

    |

  2. Prove that the line through the point (x1, y1)and parallel to the lin...

    Text Solution

    |

  3. Two lines passing through the point (2, 3) intersects each other at a...

    Text Solution

    |

  4. Find the equation of the right bisector of the line segment joining t...

    Text Solution

    |

  5. Find the coordinates of the foot of perpendicular from the point (1, 3...

    Text Solution

    |

  6. The perpendicular from the origin to the line y = m x + c meets it...

    Text Solution

    |

  7. If p and q are the lengths of perpendiculars from the origin to the l...

    Text Solution

    |

  8. In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), f...

    Text Solution

    |

  9. If p is the length of perpendicular from the origin to the line whose...

    Text Solution

    |

  10. Reduce the following equations into normal form. Find their perpendic...

    Text Solution

    |

  11. Reduce the following equations into intercept form and find their int...

    Text Solution

    |

  12. Reduce the following equations into slope intercept form and find th...

    Text Solution

    |

  13. Find equation of the line parallel to the line 3x - 4y + 2 = 0and pass...

    Text Solution

    |

  14. Find the distance between parallel lines (i) 15 x + 8y 34 = 0and 15 ...

    Text Solution

    |

  15. Find the points of the xaxis, whose distances from the line x/3+y/4=1...

    Text Solution

    |

  16. Find the distance of the point (1, 1)from the line 12(x + 6) = 5(y 2...

    Text Solution

    |

  17. Find angles between the lines sqrt(3)x+y=1and x+sqrt(3)y=1.

    Text Solution

    |

  18. Find equation of the line perpendicular to the line x - 7y + 5 = 0and ...

    Text Solution

    |