Advertisements
Advertisements
Question
Show that 2x2 + 3xy − 2y2 + 3x + y + 1 = 0 represents a pair of perpendicular lines
Solution
Comparing the given equation with the general form a = 2
h = `3/2`
b = – 2
g = `3/2`
f = `1/2`
c = 1
Condition for two lines to be perpendicular is a + b = 0.
Here a + b
= 2 – 2
= 0
⇒ The given equation represents a pair of perpendicular lines.
APPEARS IN
RELATED QUESTIONS
If the equation ax2 + 5xy – 6y2 + 12x + 5y + c = 0 represents a pair of perpendicular straight lines, find a and c.
Show that the pair of straight lines 4x2 + 12xy + 9y2 – 6x – 9y + 2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines.
If m1 and m2 are the slopes of the pair of lines given by ax2 + 2hxy + by2 = 0, then the value of m1 + m2 is:
The angle between the pair of straight lines x2 – 7xy + 4y2 = 0 is:
If the lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are the diameters of a circle, then its centre is:
Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0
Find p and q, if the following equation represents a pair of perpendicular lines
6x2 + 5xy – py2 + 7x + qy – 5 = 0
For what values of k does the equation 12x2 + 2kxy + 2y2 +11x – 5y + 2 = 0 represent two straight lines
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
Choose the correct alternative:
The length of ⊥ from the origin to the line `x/3 - y/4` = 1 is
Choose the correct alternative:
One of the equation of the lines given by x2 + 2xy cot θ – y2 = 0 is
The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A'B (where B is the point (2, 3)) subtend angle `π/4` at the origin, is equal to ______.
Let the equation of the pair of lines, y = px and y = qx, can be written as (y – px) (y – qx) = 0. Then the equation of the pair of the angle bisectors of the lines x2 – 4xy – 5y2 = 0 is ______.
The pair of lines represented by 3ax2 + 5xy + (a2 – 2)y2 = 0 are perpendicular to each other for ______.
