Advertisements
Advertisements
Question
Reduce the following equation into intercept form and find their intercepts on the axes.
4x – 3y = 6
Solution
The given equation is 4x – 3y = 6.
It can be written as
`(4"x")/6 - (3"y")/6 = 1`
`(2"x")/3 - "y"/2 = 1`
i.e., `"x"/((3/2)) + "y"/(-2) = 1` ...........(1)
This equation is of the form `"x"/"a" + "y"/"b" = 1`, where a = `3/2` and b = −2.
Therefore, equation (1) is in the intercept form, where the intercepts on the x and y axes are `3/2` and −2 respectively.
APPEARS IN
RELATED QUESTIONS
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.
If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that `1/p^2 = 1/a^2 + 1/b^2`.
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.
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
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.
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 which is equidistant from the lines x = − 2 and x = 6.
Find the equation of a line which makes an angle of tan−1 (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.
Find the lines through the point (0, 2) making angles \[\frac{\pi}{3} \text { and } \frac{2\pi}{3}\] with the x-axis. Also, find the lines parallel to them cutting the y-axis at a distance of 2 units below the origin.
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 equation of a line for p = 5, α = 60°.
Find the equation of a line for p = 4, α = 150°.
Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
Find the equation of the straight line which makes a triangle of area \[96\sqrt{3}\] with the axes and perpendicular from the origin to it makes an angle of 30° with Y-axis.
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.
Put the equation \[\frac{x}{a} + \frac{y}{b} = 1\] to the slope intercept form and find its slope and y-intercept.
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.
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 y = m1 x + c1, y = m2 x + c2 and x = 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.
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.
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.
The figure formed by the lines ax ± by ± c = 0 is
Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
A line passes through P(1, 2) such that its intercept between the axes is bisected at P. The equation of the line is ______.
If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
y − 2 = 0
