Advertisements
Advertisements
प्रश्न
Find the equation of a line that has y-intercept −4 and is parallel to the line joining (2, −5) and (1, 2).
उत्तर
Let m be the slope of the required line.
c = y-intercept = -4
It is given that the required line is parallel to the line joining the points (2, −5) and (1, 2).
Substituting the values of m and c in y = mx + c, we get, y =
Hence, the equation of the required line is 7x + y + 4 = 0
APPEARS IN
संबंधित प्रश्न
Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0. at right angle. Find the value of h.
Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
If p and q are the lengths of perpendiculars from the origin to the lines x cos θ – y sin θ = k cos 2θ and xsec θ+ y cosec θ = k, respectively, prove that p2 + 4q2 = k2.
If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that
In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?
Prove that the product of the lengths of the perpendiculars drawn from the points
Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.
Find the equation of a line for p = 8, α = 300°.
Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α =
Reduce the equation
Reduce the following equation to the normal form and find p and α in
Reduce the following equation to the normal form and find p and α in x − 3 = 0.
Put the equation
Reduce the lines 3 x − 4 y + 4 = 0 and 2 x + 4 y − 5 = 0 to the normal form and hence find which line is nearer to the origin.
Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line
Find the point of intersection of the following pairs of lines:
Find the area of the triangle formed by the line x + y − 6 = 0, x − 3y − 2 = 0 and 5x − 3y + 2 = 0.
Find 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.
Find the coordinates of the incentre and centroid of the triangle whose sides have the equations 3x− 4y = 0, 12y + 5x = 0 and y − 15 = 0.
Prove that the following sets of three lines are concurrent:
15x − 18y + 1 = 0, 12x + 10y − 3 = 0 and 6x + 66y − 11 = 0
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
Find the equation of the right bisector of the line segment joining the points (a, b) and (a1, b1).
Find the coordinates of the foot of the perpendicular from the point (−1, 3) to the line 3x − 4y − 16 = 0.
Find the projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).
The equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are x − y + 5 = 0 and x + 2y = 0 respectively. If the point A is (1, −2), find the equation of the line BC.
Determine whether the point (−3, 2) lies inside or outside the triangle whose sides are given by the equations x + y − 4 = 0, 3x − 7y + 8 = 0, 4x − y − 31 = 0 .
Write the coordinates of the orthocentre of the triangle formed by the lines xy = 0 and x + y = 1.
If the lines ax + 12y + 1 = 0, bx + 13y + 1 = 0 and cx + 14y + 1 = 0 are concurrent, then a, b, c are in
A (6, 3), B (−3, 5), C (4, −2) and D (x, 3x) are four points. If ∆ DBC : ∆ ABC = 1 : 2, then x is equal to
The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (−2, 6). The third vertex is
A point equidistant from the line 4x + 3y + 10 = 0, 5x − 12y + 26 = 0 and 7x+ 24y − 50 = 0 is
A line passes through P(1, 2) such that its intercept between the axes is bisected at P. The equation of the line is ______.
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.
If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
For specifying a straight line, how many geometrical parameters should be known?
The line which cuts off equal intercept from the axes and pass through the point (1, –2) is ______.
Reduce the following equation into intercept form and find their intercepts on the axes.
4x – 3y = 6