Let `a x+b y+c=0`be a variable straight line, whre `a , ba n dc`are the 1st, 3rd, and 7th terms of an increasing AP, respectively.Then prove that the variable straight line always passes through a fixedpoint. Find that point.

Let `a x+b y+c=0`be a variable straight line, whre `a , ba n dc`are th

1.	Let `a x+b y+c=0`be a variable straight line, whre `a , ba n dc`are the 1st, 3rd, and 7th terms of an increasing AP, respectively.Then prove that the variable straight line always passes through a fixedpoint. Find that point.
Answer» Let the common difference of A.P.be d. Then b=a+2d and c=a+6d. So, given variable straight line will be ax+(a+2d)y+a+6d=0 or a(x+y+1) + d(2y+6)=0 This is the equation of family of straight lines concurrent at point of intersection of lines x+y+1=0 and 2y+6=0 which (2,-3).

Discussion

No Comment Found

Related InterviewSolutions

Find the ratio in which the x-axis cuts the join of the points A(4,5) and B(-10,-2). Also, find the point of intersection.
If the origin is shifted to the point (-3,-2) by a translation of the axes, find the new coordinates of the point (3,-5).
The distance between the lines `5x-12y+65=0` and `5x-12y-39 = 0` is :A. 4B. 16C. 2D. 8
Prove that the locus of the centroid of the triangle whose vertices are`(acost ,asint),(bsint ,-bcost),`and `(1,0)`, where `t`is a parameter, is circle.A. `(3x -1)^(2) + (3y)^(2) = a^(2) - b^(2)`B. `(3x -1)^(2) + (3y)^(2) = a^(2) + b^(2)`C. `(3x + 1)^(2) + (3y)^(2) = a^(2) + b^(2)`D. ` (3x + 1)^(2) + (3y)^(2) = a^(2) - b^(2)`
Prove that the locus of the centroid of the triangle whose vertices are`(acost ,asint),(bsint ,-bcost),`and `(1,0)`, where `t`is a parameter, is circle.A. `(3x+1)^(2) + (3y)^(2) = a^(2) - b^(2)`B. `(3x - 1)^(2) = a^(2) - b^(2)`C. `(3x -1)^(2) + (3y)^(2) = a^(2) + b^(2)`D. `(3x + 1)^(2) + (3y)^(2) = a^(2) + b^(2)`
For `a gt b gt c gt 0`, if the distance between `(1,1)` and the point of intersection of the line `ax+by-c=0` and `bx+ay+c=0` is less than `2sqrt2` then,(A) `a+b-cgt0` (B) `a-b+clt0` (C) `a-b+cgt0` (D) `a+b-clt0`A. `a+b-c gt 0`B. `a-b+c lt 0`C. `a-b+c gt0`D. `a+b-c lt 0`
ABC is a triangle formed by the lines xy = 0 and x + y = 1 . Statement - 1 : Orthocentre of the triangle ABC is at the origin . Statement - 2 : Circumcentre of `Delta`ABC is at the point (1/2 , 1/2) .A. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 12B. Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .C. Statement-1 is True , Statement - 2 is False .D. Statement - 1 is False , Statement -2 is True .
Find the equations of the altitudes of a `triangle ABC`, whose vertices are A(2,-2), B(1,1) and C(-1,0).
The orthocentre of the triangle formed by the lines `x=2,y=3` and `3x+2y=6` is at the pointA. (2,0)B. (0,3)C. (2,3)D. none of these
If A(0, 0), B(2, 4) and C(6, 4) are the vertices of a `triangle ABC`, find the equations of its sides.

Let `a x+b y+c=0`be a variable straight line, whre `a , ba n dc`are the 1st, 3rd, and 7th terms of an increasing AP, respectively.Then prove that the variable straight line always passes through a fixedpoint. Find that point.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment