Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202519 Apr 2025Evening ShiftMathematicsStraight LinesActual

A straight line through the origin 0 meets the line 3 y =10-4 x and 8 x+6 y+5=0 at the points A and B respectively. Then 0 divides the segment A B in the ratio.

Options

  1. A4: 1
  2. B2: 3
  3. C1: 5
  4. D1: 3

Correct answer

A. 4: 1

Step-by-step solution

Let the coordinates of point A be (x_A, y_A) and point B be (x_B, y_B) . Since A lies on 3y = 10 - 4x , or equivalently 4x + 3y - 10 = 0 , we have 4x_A + 3y_A = 10 . Similarly, B lies on 8x + 6y + 5 = 0 , yielding 8x_B + 6y_B = -5 . Since the line through O , A , and B is straight and O lies between A and B , let O divide AB internally in the ratio : 1 . By the section formula, the coordinates of O(0,0) satisfy x_A + x_B + 1 = 0 and y_A + y_B + 1 = 0 , which imply x_A = - x_B and y_A = - y_B . Substituting into the

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All MHT CET PYQs