Advertisements
Advertisements
प्रश्न
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is `3/5`, its equation is ______.
विकल्प
5y – 3x + 15 = 0
3y – 5x + 15 = 0
5y – 3x – 15 = 0
None of these
उत्तर
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is `3/5`, its equation is 5y – 3x + 15 = 0.
Explanation:
Since the lines cut off intercepts – 3 on y-axis then the line is passing through the point (0, – 3).
Given that: tan θ = `3/5`
⇒ Slope of the line m = `3/5`
So, the equation of the line is y – y1 = m(x – x1)
⇒ y + 3 = `3/5(x - 0)`
⇒ 5y + 15 = 3x
⇒ 3x – 5y – 15 = 0
⇒ 5y – 3x + 15 = 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).
Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 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.
Show that the equation of the line passing through the origin and making an angle θ with the line `y = mx + c " is " y/c = (m+- tan theta)/(1 +- m tan theta)`.
Prove that the product of the lengths of the perpendiculars drawn from the points `(sqrt(a^2 - b^2), 0)` and `(-sqrta^2-b^2, 0)` to the line `x/a cos theta + y/b sin theta = 1` is `b^2`.
A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y+ 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.
Find the equation of a line which is equidistant from the lines x = − 2 and x = 6.
Find the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3).
Find the equation of the bisector of angle A of the triangle whose vertices are A (4, 3), B (0, 0) and C(2, 3).
Find the equations of the diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y =1.
Reduce the following equation to the normal form and find p and α in \[x + \sqrt{3}y - 4 = 0\] .
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.
Show that the origin is equidistant from the lines 4x + 3y + 10 = 0; 5x − 12y + 26 = 0 and 7x + 24y = 50.
Reduce the equation 3x − 2y + 6 = 0 to the intercept form and find the x and y intercepts.
Find the point of intersection of the following pairs of lines:
\[y = m_1 x + \frac{a}{m_1} \text { and }y = m_2 x + \frac{a}{m_2} .\]
Find the coordinates of the vertices of a triangle, the equations of whose sides are
y (t1 + t2) = 2x + 2a t1t2, y (t2 + t3) = 2x + 2a t2t3 and, y (t3 + t1) = 2x + 2a t1t3.
Find the area of the triangle formed by the line x + y − 6 = 0, x − 3y − 2 = 0 and 5x − 3y + 2 = 0.
Prove that the following sets of three lines are concurrent:
\[\frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1\text { and } y = x .\]
Find the projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).
Write the coordinates of the orthocentre of the triangle formed by the lines xy = 0 and x + y = 1.
Write the area of the figure formed by the lines a |x| + b |y| + c = 0.
The equations of the sides AB, BC and CA of ∆ ABC are y − x = 2, x + 2y = 1 and 3x + y + 5 = 0 respectively. The equation of the altitude through B is
If the lines x + q = 0, y − 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be
A point equidistant from the line 4x + 3y + 10 = 0, 5x − 12y + 26 = 0 and 7x+ 24y − 50 = 0 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.
The inclination of the line x – y + 3 = 0 with the positive direction of x-axis is ______.
For specifying a straight line, how many geometrical parameters should be known?
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
6x + 3y – 5 = 0
