Advertisements
Advertisements
प्रश्न
Find the point of intersection of the following pairs of lines:
2x − y + 3 = 0 and x + y − 5 = 0
उत्तर
The equations of the lines are as follows:
2x − y + 3 = 0 ... (1)
x + y − 5 = 0 ... (2)
Solving (1) and (2) using cross-multiplication method:
\[\frac{x}{5 - 3} = \frac{y}{3 + 10} = \frac{1}{2 + 1}\]
\[ \Rightarrow \frac{x}{2} = \frac{y}{13} = \frac{1}{3}\]
\[ \Rightarrow x = \frac{2}{3} \text { and y }= \frac{13}{3}\]
Hence, the point of intersection is \[\left( \frac{2}{3}, \frac{13}{3} \right)\].
APPEARS IN
संबंधित प्रश्न
Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.
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 equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
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 equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.
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 making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (1, 4), (2, −3) and (−1, −2).
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).
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 a line for p = 5, α = 60°.
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 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 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 \[x + \sqrt{3}y - 4 = 0\] .
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.
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:
bx + ay = ab and ax + by = ab.
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.
Prove that the following sets of three lines are concurrent:
3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).
If a ≠ b ≠ c, write the condition for which the equations (b − c) x + (c − a) y + (a − b) = 0 and (b3 − c3) x + (c3 − a3) y + (a3 − b3) = 0 represent the same line.
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°.
If the line `x/"a" + y/"b"` = 1 passes through the points (2, –3) and (4, –5), then (a, b) is ______.
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
The line which cuts off equal intercept from the axes and pass through the point (1, –2) 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
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
y = 0
Reduce the following equation into intercept form and find their intercepts on the axes.
3x + 2y – 12 = 0
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
