Advertisements
Advertisements
प्रश्न
Find the equation of a line which is perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and which cuts off an intercept of 4 units with the negative direction of y-axis.
उत्तर
The line perpendicular to \[\sqrt{3}x - y + 5 = 0\] is \[x + \sqrt{3}y + \lambda = 0\].
It is given that the line \[x + \sqrt{3}y + \lambda = 0\] cuts off an intercept of 4 units with the negative direction of the y-axis.
This means that the line passes through \[\left( 0, - 4 \right)\].
\[\therefore 0 - \sqrt{3} \times 4 + \lambda = 0\]
\[ \Rightarrow \lambda = 4\sqrt{3}\]
Substituting the value of \[\lambda\], we get
\[x + \sqrt{3}y + 4\sqrt{3} = 0\], which is the equation of the required line.
APPEARS IN
संबंधित प्रश्न
Reduce the following equation into intercept form and find their intercepts on the axes.
3y + 2 = 0
Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
`x – sqrt3y + 8 = 0`
Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.
If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1(c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0.
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.
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (−4, 1). Find the equation of the legs (perpendicular sides) of the triangle that are parallel to the axes.
Find the equation of a line that has y-intercept −4 and is parallel to the line joining (2, −5) and (1, 2).
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.
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 = \[\frac{1}{3}\].
Find the value of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
Reduce the following equation to the normal form and find p and α in \[x + \sqrt{3}y - 4 = 0\] .
Reduce the following equation to the normal form and find p and α in \[x + y + \sqrt{2} = 0\].
Put the equation \[\frac{x}{a} + \frac{y}{b} = 1\] to the slope intercept form and find its slope and y-intercept.
Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
Find the point of intersection of the following pairs of lines:
2x − y + 3 = 0 and x + y − 5 = 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.
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
Find the conditions that the straight lines y = m1 x + c1, y = m2 x + c2 and y = m3 x + c3 may meet in a point.
If a, b, c are in A.P., prove that the straight lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent.
Find the equation of the straight line which has y-intercept equal to \[\frac{4}{3}\] and is perpendicular to 3x − 4y + 11 = 0.
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.
Find the values of α so that the point P (α2, α) lies inside or on the triangle formed by the lines x − 5y+ 6 = 0, x − 3y + 2 = 0 and x − 2y − 3 = 0.
Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y − 4 = 0, 3x − 7y − 8 = 0 and 4x − y − 31 = 0.
Write the area of the figure formed by the lines a |x| + b |y| + c = 0.
The number of real values of λ for which the lines x − 2y + 3 = 0, λx + 3y + 1 = 0 and 4x − λy + 2 = 0 are concurrent is
The figure formed by the lines ax ± by ± c = 0 is
The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (−2, 6). The third vertex is
Find the equation of a line which passes through the point (2, 3) and makes an angle of 30° with the positive direction of x-axis.
Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
For specifying a straight line, how many geometrical parameters should be known?
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is ______.
Locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes is ______.
