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:

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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:


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




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


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


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


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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 :


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



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


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)