Question

The lines p(p2 + 1)x – y + q = 0 and (p2 + 1)2 x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for

Solution

Correct option is

Exactly one value of p

The given lines being perpendicular to a common line implies that they are parallel and hence the coefficient of x and y are proportional.

SIMILAR QUESTIONS

Q1

If the equation of the locus of a point equidistant from the points

(a1b1) and (a2b2) is (a1 – a1)x + (b1  –  b2)y + c = 0,

Then the value of c is :

Q2

The line joining the point  is produced to the point L(x, y) so that AL : LB b : a, then 

               

Q3

The vertex of a triangle are the points A(–36, 7), B(20, 7) and C(0, –8), If and I be the centoid and in center of the triangle, then GI is equal to

Q4

If a, b, c are relation by 4a2 + 9b2 – 9c2 + 12ab = 0 then the greatest distance between any two lines of the family of lines

ax + by + c = 0 is:

Q5

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the numbers of integral coordinates strictly inside the triangle (integral coordinates of both and y)

Q6

If x1x2x3 as well as y1y2y3 are in G.P. with the same common ratio, then the points (x1y1), (x2y2) and (x3y3)

Q7

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

Q8

If a, b, c are all unequal and different from one and the points  are collinear then ab + bc + ca =

Q9

Consider three points

              ,

               and

              , then

Q10

The number of integral values of m, for which the x-coordinates of the point of intersection of the lines 2x + 4y = 9 and 

y = mx + 1 is also an integral is