NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

If 5 a + 4 b + 20 c = t , then the value of t for which the line a x + b y + c - 1 = 0 always passes through a fixed point is

Options

A0
B20
C30
DNone of these

Correct answer

B. 20

Step-by-step solution

Equation of the given line is a x + b y + c − 1 = 0 ⇒ 20 a x + 20 b y + 20 c − 20 = 0 .....(i) From the given relation, substituting value of c , we get, 20 a x + 20 b y + t − 5 a − 4 b − 20 = 0 ⇒ 20 a ( x − 1 4 ) + 20 b ( y − 1 5 ) + ( t − 20 ) = 0 Clearly for t = 20 , the given line will pass through the point ( 1 4 , 1 5 ) for all the values of a & b

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point 2026 From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected r 2026 In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along the line x + y = 4 . If the orthocentre of the triangle PQR is ( , ) , then 9( + ) is equal 2026 Let P(3 , 2 ) , 0 , be a point on the ellipse x^2 9 + y^2 4 =1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the centroid of the tr 2026 Let A,B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at 2026 Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a 2026 Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is ( , ) , then 21( + ) 2026 Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to : 2026 Full Straight Lines list All NTA Abhyas JEE Main PYQs