The equation of straight line passing through (-a, 0) and making the triangle with axes of area T is
1) 2Tx + a2y + 2aT = 0 2) 2Tx – a2y + 2aT = 0 3) 2Tx – a2y... View Article
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The medians AD and BE of a triangle with vertices A(0, b), B(0, 0) and C(a, 0) are perpendicular to each other, if
1) a = √2b 2) a = -√2b 3) Both (a) and (b) 4) None of these Solution: In a... View Article
If the coordinates of the middle point of the portion of a line intercepted between coordinates axes is (3, 2), then the equation of the line will be
1) 2x + 3y = 12 2) 3x + 2y = 12 3) 4x – 3y = 6 4) 5x... View Article
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The coordinates of the point A are
1) (13/5, 0) 2) (5/13, 0) 3) (-7, 0) 4) None of these Solution: Let the incident ray meets the... View Article
The position of the points (3, 4) and (2, -6) with respect to the line 3x – 4y = 8 are
1) On the same side of the line 2) On different side of the line 3) One point on the... View Article
Choose the correct statement which describe the position of the point (-6, 2) relative to straight lines 2x + 3y – 4 = 0 and 6x + 9y + 8 = 0
1) Below both the lines 2) Above both the lines 3) In between the lines 4) None of the above... View Article
(sin θ, cos θ) and (3, 2) lies on the same side of the line x + y = 1, then θ lies between
1) (0, π/2) 2) (0, π) 3) (π/4, π/2) 4) (0, π/4) Solution: Let L be the line given by... View Article
The equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, -1). The length of the side of the triangle is
1) √(3/2) 2) √2 3) √(2/3) 4) None of these Solution: Let C(2, -1) be the vertex of the equilateral... View Article
Two lines represented by equations x + y = 1 and x + ky = 0 are mutually orthogonal if k is
1) 1 2) –1 3) 0 4) None of these Solution: Given x + y = 1 …(i) x +... View Article
The length of perpendicular from a point (1, 2) to the straight line 3x + 4y + 4 = 0
1) 5 2) 3 3) 7/5 4) None of these Solution: Given point is (1, 2) Equation of straight line... View Article
The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at (4, -3) is
1) 3x + 4y = 24 2) 3x – 4y = 12 3) 3x – 4y = 24 4) 4x... View Article
The equation of straight line equally inclined to the axes and equidistant from the points (1, -2) and (3, 4) is ax + by + c = 0 where
1) a = 1, b = 1, c = 1 2) a = 1, b = –1, c = –1... View Article
Distance between the parallel lines 3x + 4y + 7 = 0 and 3x + 4y – 5 = 0 is
1) 2/5 2) 12/5 3) 5/12 4) ⅗ Solution: Given 3x + 4y + 7 = 0 …(i) 3x +... View Article
The length of the straight line x – 3y = 1 intercepted by the hyperbola x2 – 4y2 = 1, is
1) √10 2) 6/5 3) 1/√10 4) (6/5)√10 Solution: Given line is x – 3y = 1 => x =... View Article
The distance of the lines 2x – 3y = 4 from the point (1, 1) measured parallel to the line x + y = 1 is
1) √2 2) 5/√2 3) 1/√2 4) 6 Solution: Given x + y = 1 ..(i) Let the equation of... View Article
The distance of the point (-2, 3) from the line x – y = 5 is
1) 5√2 2) 2√5 3) 3√5 4) 5√3 Solution: We know that the distance of a point P(x1, y1) from... View Article
If the line y = 7x – 25 meets the circle x2 + y2 = 25 in the points A, B, then the distance between A and B is
1) √10 2) 10 3) 5√2 4) 5 Solution: Given line is y = 7x – 25 …(i) Equation of... View Article
The distance between 4x + 3y = 11 and 8x + 6y = 15, is
1) 7/2 2) 4 3) 7/10 4) None of these Solution: Given 4x + 3y = 11 ..(i) 8x +... View Article
The perpendicular distance of the straight line 12x + 5y = 7 from the origin is given by
1) 7/13 2)12/13 3) 5/13 4) 1/13 Solution: We know that the length of the perpendicular from origin (0, 0)... View Article
If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then
1) a2 + b2 = p2 2) a2 + b2 = 1/p2 3) 1/a2 + 1/b2 = 2/p2 4) 1/a2... View Article
