Condition of Concurrency of 3 Straight Lines
Trending Questions
Q. Area of triangle with adjacent sides determined by a vector and b vector is 20 . Then area of triangle with adjacent sides determined by vectors ( 2a + 3b ) and ( a - b) is
Q. If the pairs of lines x^2+2xy+ay^2=0 and ax^2+2xy+y^2=0 have exactly one line in common then the joint equation of the other two lines is given by1) 3x^2+8xy-3y^2=0 2) 3x^2+10xy+3y^2=03) y^2+2xy-3x^2=0 4) x^2+2xy-3y^2=0
Q.
Show that the points (−2, 3, 5), (1, 2, 3) and (7, 0, −1) are collinear.
Q.
Verify that the points (3, -2, 4), (1, 0, -2) and (-1, 2, -8) are collinear.
Q. 50. The points (5, 0), (0, 12), (-5, 0) are the vertices of an isosceles triangle. Then the equation of its incircle is?
Q. 39. Through the point (3, 4) are drawn two straight lines each inclined at 45^° to the straight line x - y = 2. Find their equations and find also the area included by the three lines.
Q. The radius of the circle which touches line y = x at (2, 2) and also touches the y-axis is/are – (1) 4(\sqrt2 + 1) (2) 4 – 2\sqrt2(3) 4 + 2\sqrt2 (4) 4(\sqrt2 – 1)
Q. 15. If the lines ax+y+1=0, x+by+1=0, x+y+c=0 (a, b and c are distinct and different from 1) are concurrent then the value of a/(a-1) + b/(b-1) + c/(c-1) is a)0. b)1. c)2. d)3.
Q. a(-1, 1), b(5, 3) are opposite vertices of a square.the equation of the other diagonal (not passing through a, b) of a square is?
Q. The value(s) of a for which the lines 2x + y - 1 = 0; ax + 3y - 3 = 0 and 3x + 2y - 2 = 0 are concurrent, is/are:
- 1
- 2
- 3
- 4
- 5
Q. Q.10. Find the vector equation of the plane passing through the points (1, 1, 1), (1, - 1, 1) and (- 7, - 3, - 5).
Q. If a, b, c are in A.P., prove that the straight lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent.
Q. The number of value of k, for which the system the system of equation (k + 1)x + 8y = 4k ⇒ kx + (k + 3)y = 3k - 1 has no solution, is
- infinite
- 1
- 2
- 3
Q. Prove that the following sets of three lines are concurrent:
(i) 15x − 18y + 1 = 0, 12x + 10y − 3 = 0 and 6x + 66y − 11 = 0
(ii) 3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
(iii)
(i) 15x − 18y + 1 = 0, 12x + 10y − 3 = 0 and 6x + 66y − 11 = 0
(ii) 3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0
(iii)
Q.
The distance of (0, 0) from the line x+y=1 is
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2 units
3 units
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