If 3a +2b+c=0 for all positions of the moving line ax+by+c=0 , show that the line always passes through a fixed point . Find the coordinates of that fixed point.
Text Solution
Verified by Experts
The correct Answer is:
`(3,2)`
Topper's Solved these Questions
STRAIGHT LINE
CHHAYA PUBLICATION|Exercise EXERCISE 2A (Multiple Choice Type Questions)|20 Videos
STRAIGHT LINE
CHHAYA PUBLICATION|Exercise EXERCISE 2A(Very Short Answer Type Questions)|14 Videos
MATHEMATICAL INDUCTION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos
Similar Questions
Explore conceptually related problems
If a+b+c=0 for all positions of the moving line ax+by+c=0 , show that the line always passes throught a fixed point . Find the coordinates of that fixed point.
Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes through a fixed point , find the cootdinates of that fixed point.
Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always passes through a fixed point. Find the co-ordinate of that point.
If a + 2b + 3c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point, find the co-ordinates of fixed point.
Show that all chords of the curve 3x^2-y^2-2x+4y=0, which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.
If a+b+c=0, then the straight lines 4ax + 3by+c=0 always pass through a fixed whose coordinates are-
If 3a+2b+6c=0, the family of straight lines ax+by+c=0 passes through a fixed point whose coordinates are given by
If a, b ,c are in A.P ., then the straight line ax + 2by + c=0 will always pass through a fixed point whose coordinates are
If a , b ,c are in harmonic progression, then the straight line (x/a)+(y/b)+(1/c)=0 always passes through a fixed point. Find that point.
The centre of the circle S = 0 lies on the line 2x -2y + 9 = 0 and S = 0 cuts orthogonally the circle x^2 + y^2 = 4 . Show that S = 0 passes through two fixed points and also find the co-ordinates of these two points.
CHHAYA PUBLICATION-STRAIGHT LINE-Sample Questions for Competitive Exams (Assertion-Reason Type)