Advertisements
Advertisements
प्रश्न
A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units
Advertisements
उत्तर
Let the given line be PQ whose equation is
5x = y + 7
5x – y – 7 = 0 ......(1)
Let AB be the line perpendicular to the line PQ such that the area of the triangle OAB is 10 units.
The equation of the line AB is
– x – 5y + k = 0
x + 5y – k = 0
x + 5y = k ......(2)
`x/"l" + (5y)/"k"` = 1
`x/"k" + y/("k"/5)` = 1
∴ A is (k, 0) and B is `(0, "k"/5)`
OA = k and OB = `"k"/5`
Area of ∆OAB = `1/2 xx "OA" xx "OB"`
= `1/2 xx "k" xx "k"/5`
Given area of ∆OAB = 10
∴ `("k"^2)/10` = 10
k2 = 100
⇒ k = ±10
∴ The required equation of the straight line is
x + 5y = ±10
APPEARS IN
संबंधित प्रश्न
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3
Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)
Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0
If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and parallel to x − y + 5 = 0
Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10, −2) to the line x + y − 2 = 0
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A
Find the image of the point (−2, 3) about the line x + 2y − 9 = 0
A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Find the cost of making 40 copies
Choose the correct alternative:
The slope of the line which makes an angle 45° with the line 3x − y = −5 are
Choose the correct alternative:
The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is
Choose the correct alternative:
If the two straight lines x + (2k − 7)y + 3 = 0 and 3kx + 9y − 5 = 0 are perpendicular then the value of k is
Choose the correct alternative:
If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is
