02%20-%20Line-Lines

02%20-%20Line-Lines - PROBLEMS (1) 02 - LINE / LINES Find...

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PROBLEMS 02 - LINE / LINES Page 1 ( 1 ) Find the parametric equations of the line passing through A ( 3, - 2 ) and B ( - 4, 5 ) and hence express AB, AB and AB as sets. + + + = + = = = = } AB and } AB }, Further . R t , 1 t 0 ) 2 7t 3, 7t ( { R t 0, t ) 2 7t 3, 7t ( { R t ) 2 7t 3, 7t ( { AB R t 2, 7t y 3, 7t x are AB of equations Parametric : Ans l l l - - - - - - - - ( 2 ) If the length of the perpendicular segment from the origin is 10 and α = - 6 5 π , then find the equation of the line. [ Ans: 3 x + y + 20 = 0 ] ( 3 ) If the lines 3x + y + 4 = 0, 3x + 4y - 15 = 0 and 24x - 7y - 3 = 0 contain the sides of a triangle, prove that the triangle is isosceles. ( 4 ) Find the co-ordinates of the point at a distance of 10 units from the point ( 4, - 3 ) on the line perpendicular to 3x + 4y = 0. [ Ans: ( 10, 5 ), ( - 2, - 11 ) ] ( 5 ) A ( x 1 , y 1 ) and B ( x 2 , y 2 ) are points of the plane. If the line ax + by + c = 0 divides AB, find the ratio in which it divides AB from A. + + + + + + : λ = - 0 c by ax , c by ax c by ax 1 : Ans 2 2 2 2 1 1 ( 6 ) If the sum of the intercepts on the axes of a line is constant, find the equation satisfied by the mid-point of the segment of the line intercepted between the axes. [ Ans: x + y = k, where 2k = constant sum of the intercepts ] ( 7 ) Find k if the lines kx - y - 2 = 0, 2x + ky - 5 = 0 and 4x - y - 3 = 0 are concurrent. [ Ans: k = 3 or - 2 ]
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PROBLEMS 02 - LINE / LINES Page 2 ( 8 ) Among all the lines passing through the point of intersection of the lines x + y - 7 = 0 and 4x - 3y = 0, find the one for which the length of the perpendicular segment on it from the origin is maximum. [ Ans: 3x + 4y - 25 = 0 ] ( 9 ) Prove that the product of the perpendicular distances of the line θ sin b y θ cos a x + = 1 from the points ± 0 , b 2 a 2 - is b 2 . ( 10 ) Prove that if l m 1 l 1 m, n n 1 and l 2 + m 2 = l 1 2 + m 1 2 , then the lines l x + my + n = 0, l 1 x + m 1 y + n 1 = 0, l x + my + n 1 = 0 and l 1 x + m 1 y + n = 0 form a rhombus. ( 11 ) Prove that the lines ( a 2 - 3b 2 ) x 2 + 8abxy + ( b 2 - 3a 2 ) y 2 = 0 and ax + by + c = 0, c 0 contain the sides of an equilateral triangle whose area is ) b a ( 3 c 2 2 2 + . ( 12 ) Two lines are represented by 3x 2 - 7xy + 2y 2 - 14x + 13y + 15 = 0. Find the measure of the angle between them and the point of their intersection. π 5 4 , 5 7 , 4 : Ans - ( 13 ) If the intercepts on the axes by the line x cos α + y sin α = p are a and b, prove that a - 2 + b - 2 = p - 2 . ( 14 )
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02%20-%20Line-Lines - PROBLEMS (1) 02 - LINE / LINES Find...

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