Advertisements
Advertisements
प्रश्न
Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.
उत्तर
Intercept form of straight-line `x/a + y/b` = 1
Where a and b are the intercepts on the axis
Given that a = b
∴ `x/a + y/a` = 1 ....(i)
If equation (i) passes through the point (1, – 2), we get
`1/a - 2/a` = 1
⇒ `-1/a` = 1
⇒ a = – 1
So, equation of the straight line is
`x/(-1) + y/(-1)` = 1
⇒ x + y = – 1
⇒ x + y + 1 = 0
Hence, the required equation is x + y + 1 = 0.
APPEARS IN
संबंधित प्रश्न
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 perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
Find angles between the lines `sqrt3x + y = 1 and x + sqrt3y = 1`.
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 `(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`.
Find the equation of a line for p = 5, α = 60°.
Find the equation of a line for p = 8, α = 225°.
Find the equation of a straight line on which the perpendicular from the origin makes an angle of 30° with x-axis and which forms a triangle of area \[50/\sqrt{3}\] with the axes.
Reduce the equation\[\sqrt{3}\] x + y + 2 = 0 to intercept form and find intercept on the axes.
Reduce the following equation to the normal form and find p and α in \[x + y + \sqrt{2} = 0\].
Reduce the following equation to the normal form and find p and α in \[x - y + 2\sqrt{2} = 0\].
Reduce the following equation to the normal form and find p and α in x − 3 = 0.
Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
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:
2x − y + 3 = 0 and x + y − 5 = 0
Find the coordinates of the vertices of a triangle, the equations of whose sides are x + y − 4 = 0, 2x − y + 3 = 0 and x − 3y + 2 = 0.
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 coordinates of the incentre and centroid of the triangle whose sides have the equations 3x− 4y = 0, 12y + 5x = 0 and y − 15 = 0.
Find the equation of the right bisector of the line segment joining the points (a, b) and (a1, b1).
Find the image of the point (2, 1) with respect to the line mirror x + y − 5 = 0.
Find the projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).
Write the area of the figure formed by the lines a |x| + b |y| + c = 0.
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.
Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants.
If the line `x/"a" + y/"b"` = 1 passes through the points (2, –3) and (4, –5), then (a, b) is ______.
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 ______.
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
x + 7y = 0
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
6x + 3y – 5 = 0
