Advertisements
Advertisements
प्रश्न
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.
उत्तर
The given equation are ax + by + 8 = 0 ......(i)
And 2x – 3y + 6 = 0 ......(ii)
From equation (i) we get,
ax + by + 8 = 0
⇒ `a/(-8)x + b/(-8)y` = 1
⇒ `x/((-8)/a) + y/((-8)/b)` = 1
So, the intercepts on the axes are `(-8)/a` and `(-8)/b`
From equation (ii), we get
2x – 3y + 6 = 0
⇒ 2x – 3y = – 6
⇒ `(2x)/(6) - (3y)/(-6)` = 1
⇒ `x/(-3) + y/2` = 1
So, the intercepts are – 3 and 2.
`(-8)/a` = + 3
⇒ a = ` - 8/3`
⇒ `(-8)/b` = – 2
⇒ b = + 4
Hence, the required values of a and b are `(-8)/3` and 4.
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.
The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0. at right angle. Find the value of h.
Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.
Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.
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.
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 the bisector of angle A of the triangle whose vertices are A (4, 3), B (0, 0) and C(2, 3).
Point R (h, k) divides a line segment between the axes in the ratio 1 : 2. Find the equation of the line.
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 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 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 y − 2 = 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.
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 lines \[y = \sqrt{3}x + 1, y = 4 \text { and } y = - \sqrt{3}x + 2\] form an equilateral triangle.
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
Prove that the following sets of three lines are concurrent:
\[\frac{x}{a} + \frac{y}{b} = 1, \frac{x}{b} + \frac{y}{a} = 1\text { and } y = x .\]
Show that the straight lines L1 = (b + c) x + ay + 1 = 0, L2 = (c + a) x + by + 1 = 0 and L3 = (a + b) x + cy + 1 = 0 are concurrent.
If the three lines ax + a2y + 1 = 0, bx + b2y + 1 = 0 and cx + c2y + 1 = 0 are concurrent, show that at least two of three constants a, b, c are equal.
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 area of the figure formed by the lines a |x| + b |y| + c = 0.
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°.
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?
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is ______.
Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
x − y = 4
