हिंदी

Find the Equation of the Straight Lines Passing Through the Following Pair of Point : (0, −A) and (B, 0)

Advertisements
Advertisements

प्रश्न

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

(0, −a) and (b, 0)

संक्षेप में उत्तर
Advertisements

उत्तर

 (0, −a) and (b, 0) 

\[\text { Here,} \left( x_1 , y_1 \right) \equiv \left( 0, - a \right) \]

\[\left( x_2 , y_2 \right) \equiv \left( b, 0 \right)\]

So, the equation of the line passing through the two points is

\[y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}\left( x - x_1 \right)\]

\[ \Rightarrow y + a = \frac{0 + a}{b - 0}\left( x - 0 \right)\]

\[ \Rightarrow ax - by = ab\]

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 23.5 [पृष्ठ ३५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.5 | Q 1.3 | पृष्ठ ३५

संबंधित प्रश्न

Find the equation of the line parallel to x-axis and passing through (3, −5).


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


Find the equation of the straight line passing through (−2, 3) and inclined at an angle of 45° with the x-axis.


Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.


Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x-axis whose sine is \[\frac{3}{5}\].


Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.


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.


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


In what ratio is the line joining the points (2, 3) and (4, −5) divided by the line passing through the points (6, 8) and (−3, −2).


The length L (in centimeters) of a copper rod is a linear function of its celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.


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


Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes
(i) equal in magnitude and both positive,
(ii) equal in magnitude but opposite in sign.


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.


The straight line through P (x1, y1) inclined at an angle θ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.


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.


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 through the point (α, β) and perpendicular to the line lx + my + n = 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 origin and are inclined at an angle of 75° to the straight line \[x + y + \sqrt{3}\left( y - x \right) = a\].


Find the equations of the straight lines passing through (2, −1) and making an angle of 45° with the line 6x + 5y − 8 = 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.


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 passing through the point of intersection of 2x + y − 1 = 0 and x + 3y − 2 = 0 and making with the coordinate axes a triangle of area \[\frac{3}{8}\] sq. units.


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


A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is


Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.


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.


Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×