Question

If the gradient of one of the lines given by  is twice that of the other, then h =  

Solution

Correct option is

±3

 

Let m and 2m be the gradients of the lines given by the equation x2 + hxy+ 2y2 = 0. Then, 

        

.

SIMILAR QUESTIONS

Q1

The straight lines joining the origin to the points of intersection of the linekx + hy = 2hk with the curve (x – h)2 + (y – k)2 = c2 are at right angles, if

Q2

If the lines joining the origin to the points of intersection of the line y = mx+ 2 and the curve x2 + y2 = 1 are at right-angles, then

Q3

The equation  represents a The Pair of Straight Lines, if

Q4

The equation  represents a The Pair of Straight Lines passing through the origin. The two lines are

Q5

If the pairs of straight lines ax2 + 2hxy – ay2 = 0 and bx2 + 2gxy – by2 = 0 be such that each bisects the angles between the other, then

Q6

If  represents parallel straight lines, then

Q7

 

If the equation  represents a pair of perpendicular straight lines, then  

 

Q8

The equation  represents a The Pair of Straight Lines. The distance between them is

Q9

 

Let PQR be a right angled isosceles triangle, right angled at

P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is   

Q10

The set of values of h for which the equation  represents a pair of real and distinct lines is