Advertisements
Advertisements
प्रश्न
Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
Advertisements
उत्तर
Let the equation of line AB be: x – 2y = 3
or y = `1/2 "x" - 3`
Then the slope of line AB = `1/2`
Let the PA line make an angle of 45° with it and its slope = m.
`± tan 45= ("m" - 1/2)/(1 + "m" xx 1/2)`
or `± 1 = (2"m" - 1)/("m" + 2)`
Taking +ve sign, 1 = `(2"m" - 1)/("m" + 2)`
or 2m – 1 = m + 2
∴ m = 3
2m –1
Taking – ve sign, –1 = `(2"m" - 1)/("m" + 2)`
or 2m – 1 = –m – 2
∴ 3m = –1
or m = `(-1)/3`
Hence, the equation of line PA is where point P = (3, 2) and m = `(-1)/3`.
y – 2 = `- (-1)/3 ("x" - 3)`
3y – 6 = – x + 3
or x + 3y – 9 = 0
Now when the slope is m = 3, then the equation of the line from the point P(3, 2),
y – 2 = 3(x – 3)
y – 2 = 3x – 9
or 3x – y – 7 = 0
APPEARS IN
संबंधित प्रश्न
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
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: \[\frac{\pi}{3}\]
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
Find the slope of a line passing through the following point:
(3, −5), and (1, 2)
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?
What can be said regarding a line if its slope is zero ?
Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
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 points (2, −1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.
If x + y = k is normal to y2 = 12x, then k is ______.
Point of the curve y2 = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is ______.
The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
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 line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.
Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
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 ______.
