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.
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)
APPEARS IN
संबंधित प्रश्न
Find the equation of the line parallel to x-axis and passing through (3, −5).
Find the equation of the line perpendicular to x-axis and having intercept − 2 on x-axis.
Find the equation of a line equidistant from the lines y = 10 and y = − 2.
Find the equation of the line passing through (0, 0) with slope m.
Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.
Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).
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 :
(at1, a/t1) and (at2, a/t2)
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.
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 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 straight line which passes through the point (−3, 8) and cuts off positive intercepts on the coordinate axes whose sum is 7.
Find the equation of a line which passes through the point (22, −6) and is such that the intercept of x-axis exceeds the intercept of y-axis by 5.
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 equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a − b = 2.
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.
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 origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin β).
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 distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x − 3y = 7.
The equation of one side of an equilateral triangle is x − y = 0 and one vertex is \[(2 + \sqrt{3}, 5)\]. Prove that a second side is \[y + (2 - \sqrt{3}) x = 6\] and find the equation of the third side.
Two sides of an isosceles triangle are given by the equations 7x − y + 3 = 0 and x + y − 3 = 0 and its third side passes through the point (1, −10). Determine the equation of the third side.
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.
Find the equation of the straight line which passes through the point of intersection of the lines 3x − y = 5 and x + 3y = 1 and makes equal and positive intercepts on the axes.
Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is \[\sqrt{5}\].
Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.
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.
Find the locus of the mid-points of the portion of the line x sinθ+ y cosθ = p intercepted between the axes.
If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 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 straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.
