Question

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:

Solution

Correct option is

∴  (2a + 3b + 3c) (2a + 3b – 3c) = 0

  

Above shown that the given line ax + by + c = 0 passes through the points  and distance between them is

       

SIMILAR QUESTIONS

Q1

If the origin is shifted to (1, –2), the coordinates of A become (2, 3). What are the original coordinates of A?

Q2

Determiner as to what point the axes of the coordinates be shifted so as to remove the first degree terms from the equation

           (x, y) = 2x2 + 3y2 – 12x + 12+ 24 = 0

Q3

What will be the coordinates of the point  when the axes are rotated through an angle of 300 in clockwise sense?

Q4

What will be the coordinates of the point in original position ifr its coordinates after rotation of axes through an angle 600  ?

Q5

The in centre of the triangle with vertices , (0, 0) and (2, 0) is

Q6

If a vertex of a triangle is (1, 1) and the mid-point of two sides through the vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

Q7

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 :

Q8

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

               

Q9

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

Q10

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)