Advertisements
Advertisements
Question
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
Advertisements
Solution
Given that the line makes angle 30° with y-axis
∴ Angle made by the line with x-axis is 60°
∴ Slope of the line
m = tan 60°
⇒ m = `sqrt(3)`
So, the equation of the line passing through the point (1, 2)
And slope `sqrt(3)` is y – y1 = m(x – x1)
⇒ y – 2 = `sqrt(3)(x - 1)`
⇒ y – 2 = `sqrt(3)(x - 1)`
⇒ `y - sqrt(3)x + sqrt(3) - 2` = 0
Hence, the required equation of line is `y - sqrt(3)x + sqrt(3) - 2` = 0
APPEARS IN
RELATED QUESTIONS
Find the equation of the line parallel to x-axis and passing through (3, −5).
Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.
Find the equation of the straight line passing through the point (6, 2) and having slope − 3.
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 passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
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)
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).
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 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 the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Find the equation of straight line passing through (−2, −7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
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.
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 line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
Find the equation of a line passing through (3, −2) and perpendicular to the line x − 3y + 5 = 0.
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 equation of the straight lines passing through the origin and making an angle of 45° with the straight line \[\sqrt{3}x + y = 11\].
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.
Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenues is 3x + 4y = 4 and the opposite vertex is the point (2, 2).
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.
The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, −1). Find the length and equations of its sides.
Find the equation of the straight line drawn through the point of intersection of the lines x + y = 4 and 2x − 3y = 1 and perpendicular to the line cutting off intercepts 5, 6 on the axes.
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.
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 the diagonals of the quadrilateral formed by the lines l1x + m1y + n1 = 0, l2x + m2y + n2 = 0, l1x + m1y + n1' = 0 and l2x + m2y + n2' = 0 are perpendicular, then write the value of l12 − l22 + m12 − m22.
If the point (5, 2) bisects the intercept of a line between the axes, then its equation 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.
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 ______.
