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
Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3
Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0
Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6
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 equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and perpendicular to x − 2y + 1 = 0
If p1 and p2 are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p12 + p22 = a2
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Find the family of straight lines parallel to 3x + 4y – 12
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position
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. Draw graph of the cost as x goes from 0 to 50 copies
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 intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are
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
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
