हिंदी

If A, B, C Are in A.P., Then the Line Ax + by + C = 0 Passes Through a Fixed Point. Write the Coordinates of that Point.

Advertisements
Advertisements

प्रश्न

If a, b, c are in A.P., then the line ax + by + c = 0 passes through a fixed point. Write the coordinates of that point.

संक्षेप में उत्तर
Advertisements

उत्तर

If, a, b, c are in A.P, then
a + c = 2b
⇒ a − 2b + c = 0
Comparing the coefficient of  ax + by + c = 0 and a − 2b + c = 0, we get
x = 1 and y = −2
So, the the coordinates of that point is (1, −2)

shaalaa.com
Equations of Line in Different Forms - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: The straight lines - Exercise 23.20 [पृष्ठ १३२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.20 | Q 16 | पृष्ठ १३२

संबंधित प्रश्न

Find the equation of the line perpendicular to x-axis and having intercept − 2 on x-axis.


Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.


Find the equation of the straight lines passing through the following pair of point :

(a, b) and (a + b, a − b)


Find the equation of the straight lines passing through the following pair of point :

(a cos α, a sin α) and (a cos β, a sin β)


Find the equations of the sides of the triangles the coordinates of whose angular point is  respectively  (0, 1), (2, 0) and (−1, −2).


By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.


Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3 x + y = 12 which is intercepted between the axes of coordinates.


Find the equation of the straight line which passes through (1, −2) and cuts off equal intercepts on the axes.


Find the equation of the line which passes through the point (− 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point. 


Find the equation of the line, which passes through P (1, −7) and meets the axes at A and Brespectively so that 4 AP − 3 BP = 0.


Find the equation of the straight line passing through the origin and bisecting the portion of the line ax + by + c = 0 intercepted between the coordinate axes.


A straight line drawn through the point A (2, 1) making an angle π/4 with positive x-axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.


Find the equation of the line passing through the point of intersection of the lines 4x − 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes.


If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.


Three sides AB, BC and CA of a triangle ABC are 5x − 3y + 2 = 0, x − 3y − 2 = 0 and x + y − 6 = 0 respectively. Find the equation of the altitude through the vertex A.


Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .


Find the equation of the straight line perpendicular to 5x − 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).


Find the length of the perpendicular from the point (4, −7) to the line joining the origin and the point of intersection of the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0.


Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan−1 m to the straight line y = mx + c.


Prove that the family of lines represented by x (1 + λ) + y (2 − λ) + 5 = 0, λ being arbitrary, pass through a fixed point. Also, find the fixed point.


Write the area of the triangle formed by the coordinate axes and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2.


If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.


Write the equation of the line passing through the point (1, −2) and cutting off equal intercepts from the axes.


Find the locus of the mid-points of the portion of the line x sinθ+ y cosθ = p intercepted between the axes.


If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point


If the point (5, 2) bisects the intercept of a line between the axes, then its equation is


The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is


The inclination of the straight line passing through the point (−3, 6) and the mid-point of the line joining the point (4, −5) and (−2, 9) is


Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.


The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3)  x + y` = 1 is ______.


Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.


The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).


The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×