Straight Lines questions
982 published questions with worked solutions.
- Let a and b be non-zero real numbers. Then, the equation (ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0 represents
- A ray of light along x + 3 y = 3 gets reflected upon reaching x-axis, the equation of the reflected ray is -
- Among the statements (S1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose orthocentre is (0,0), then its third...
- A rectangle is formed by the lines x=0, y=0, x=3 and y=4. Let the line L be perpendicular to 3x+y+6=0 and divide the area of the...
- Let A(1,0), B(2,-1) and C ( 7 3 , 4 3 ) be three points. If the equation of the bisector of the angle ABC is x + y = 5, then the...
- Let PQR be a triangle such that PQ = -2 i - j +2 k and PR = a i +b j -4 k , a,b Z. Let S be the point on QR, which is equidistant...
- Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1) and (2, 4) in the line x + 2y = 2. If the centroid...
- Let A(6, 8), B(10 , -10 ) and C(-10 , 10 ), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid...
- A rod of length eight units moves such that its ends A and B always lie on the lines x – y + 2 = 0 and y + 2 = 0, respectively....
- Let the area of a ΔPQR with vertices P(5, 4), Q(–2, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are O (2,...
- Let the lines 3x - 4y - = 0, 8x - 11y - 33 = 0, and 2x - 3y + = 0 be concurrent. If the image of the point (1, 2) in the line 2x...
- Let ^nC_ r-1 = 28, ^nC_r = 56 and ^nC_ r+1 = 70. Let A(4cost, 4sint), B(2sint, –2cost) and C(3r – n, r^2 – n – 1) be the vertices...
- If = 1 + _ r=1 ^ 6 (-3)^ r-1 ^ 12 C_ 2r-1 , then the distance of the point (12, 3 ) from the line x - 3 y + 1 = 0 is
- Two equal sides of an isosceles triangle are along – x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum,...
- Let ABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y –31 = 0 and 9x –2y–19 = 0, Let the point (h,k) be the image of...
- Let A(4, –2), B(1, 1) and C(9, –3) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed...
- Consider the lines x(3 + 1) + y(7 + 2) = 17 + 5, being a parameter, all passing through a point P. One of these lines (say L) is...
- If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x – 8 and y = mx + c is at (3, –1), then m – c is:
- In a triangle ABC, the line joining the circumcentre to the incentre is parallel to BC. Then B+ C=
- If x=X -Y , y=X +Y and x^2+4xy+y^2=AX^2+BY^2, 0 2 , then
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