Advertisements
Advertisements
प्रश्न
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
विकल्प
y + 2 = x + 1
y + 2 = 3 (x + 1)
y – 2 = 3 (x – 1)
y – 2 = x – 1
Advertisements
उत्तर
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is y – 2 = 3 (x – 1).
Explanation:
Given equation is y = 3x – 1
Slope = 3
Slope of the line passing through the given point (1, 2) and parallel to the given line = 3
So, the equation of the required line is y – 2 = 3(x – 1)
APPEARS IN
संबंधित प्रश्न
The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[- \frac{\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].
Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).
By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the equation of a straight line with slope − 1/3 and y-intercept − 4.
Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the angles between the following pair of straight lines:
3x + y + 12 = 0 and x + 2y − 1 = 0
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Find the angles between the following pair of straight lines:
x − 4y = 3 and 6x − y = 11
Find the acute angle between the lines 2x − y + 3 = 0 and x + y + 2 = 0.
Prove that the straight lines (a + b) x + (a − b ) y = 2ab, (a − b) x + (a + b) y = 2ab and x + y = 0 form an isosceles triangle whose vertical angle is 2 tan−1 \[\left( \frac{a}{b} \right)\].
Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.
If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.
The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
