Advertisements
Advertisements
प्रश्न
Reduce the following equation into intercept form and find their intercepts on the axes.
3x + 2y – 12 = 0
उत्तर
The given equation is 3x + 2y – 12 = 0.
It can be written as
3x + 2y – 12
`(3"x")/12 + (2"y")/12 = 1`
i.e. `"x"/4 + "y"/6 = 1` ..........(1)
This equation is of the form `"x"/"a" +"y"/"b" = 1`, where a = 4 and b = 6.
Therefore, equation (1) is in the intercept form, where the intercepts on the x and y axes are 4 and 6 respectively.
APPEARS IN
संबंधित प्रश्न
Reduce the following equation into intercept form and find their intercepts on the axes.
3y + 2 = 0
Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
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 the side BC of the triangle ABC whose vertices are (−1, −2), (0, 1) and (2, 0) respectively. Also, find the equation of the median through (−1, −2).
The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150° with the positive direction of Y-axis. Find the equation of the line.
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 equation \[\sqrt{3}\] x + y + 2 = 0 to slope-intercept form and find slope and y-intercept;
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 \[x + y + \sqrt{2} = 0\].
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 x + y − 4 = 0, 2x − y + 3 = 0 and x − 3y + 2 = 0.
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 y = 0, x = 2 and x + 2y = 3.
Show that the area of the triangle formed by the lines y = m1 x, y = m2 x and y = c is equal to \[\frac{c^2}{4}\left( \sqrt{33} + \sqrt{11} \right),\] where m1, m2 are the roots of the equation \[x^2 + \left( \sqrt{3} + 2 \right)x + \sqrt{3} - 1 = 0 .\]
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:
\[\frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1\text { and } y = x .\]
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.
Find the equation of the straight line perpendicular to 2x − 3y = 5 and cutting off an intercept 1 on the positive direction of the x-axis.
Find the equation of the straight line which has y-intercept equal to \[\frac{4}{3}\] and is perpendicular to 3x − 4y + 11 = 0.
If the image of the point (2, 1) with respect to the line mirror be (5, 2), find the equation of the mirror.
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
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
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.
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 ______.
Locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes 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 intercept form and find their intercepts on the axes.
4x – 3y = 6