Advertisements
Advertisements
Question
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is three times the other, show that 3h2 = 4ab
Solution
The equation of the given straight line is
ax2 + 2hxy + by2 = 0 .......(1)
Given that the slopes of the lines are m and 3m.
∴ m + 3m = `- (2"h")/"b"`
(m)(3m) = `"a"/"b"`
4m = `- (2"h")/"b"`
and
3m2 = `"a"/"b"`
m = `- "h"/(2"b")`
⇒ `3(- "h"/(2"b"))^3 = "a"/"b"`
⇒ `3 "h"^2/(4"b"^2) = "a"/"b"`
⇒ 3h2 = 4ab
APPEARS IN
RELATED QUESTIONS
Show that the equation 12x2 – 10xy + 2y2 + 14x – 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.
Find the angle between the pair of straight lines 3x2 – 5xy – 2y2 + 17x + y + 10 = 0.
The angle between the pair of straight lines x2 – 7xy + 4y2 = 0 is:
Show that 4x2 + 4xy + y2 − 6x − 3y − 4 = 0 represents a pair of parallel lines
Show that 2x2 + 3xy − 2y2 + 3x + y + 1 = 0 represents a pair of perpendicular lines
Show that the equation 2x2 − xy − 3y2 − 6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan−1(5)
Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x − 3y + 1 = 0 and 5x + y − 3 = 0
Find the separate equation of the following pair of straight lines
2x2 – xy – 3y2 – 6x + 19y – 20 = 0
The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is twice that of the other, show that 8h2 = 9ab
Find p and q, if the following equation represents a pair of perpendicular lines
6x2 + 5xy – py2 + 7x + qy – 5 = 0
Prove that the straight lines joining the origin to the points of intersection of 3x2 + 5xy – 3y2 + 2x + 3y = 0 and 3x – 2y – 1 = 0 are at right angles
Choose the correct alternative:
Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter `4 + 2sqrt(2)` is
Choose the correct alternative:
The coordinates of the four vertices of a quadrilateral are (−2, 4), (−1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (−1, 2) and dividing the quadrilateral in the equal areas is
Choose the correct alternative:
If the equation of the base opposite to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length of a side is
Choose the correct alternative:
The image of the point (2, 3) in the line y = −x is
The pair of lines represented by 3ax2 + 5xy + (a2 – 2)y2 = 0 are perpendicular to each other for ______.
