Maths

24. A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path [...]

23. Prove that the product of the lengths of the perpendiculars drawn from the points ( sqrt a^2 – b^2,0) and (- sqrt a^2 – b^2,0) to the line x/a cosθ + y/b sinθ = 1 is b^2. 0) and (- sqrt a^2 - b^2 0) to the line x/a cosθ + y/b sinθ = [...]

22. A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A. 2) reflects on the x-axis at point A and the reflected ray passes through the point (5 22. A ray of light [...]

21. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0. 21. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0. October [...]

20. If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y +7 = 0 is always 10. Show that P must move on a line 20. If sum of the perpendicular distances of a variable point P (x [...]

19. If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m. 19. If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4 [...]

18. Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror 18. Find the image of the point (3 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror October 30, 2021 [...]

17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle. 1). Find an equation of the legs (perpendicular sides) of the triangle. 17. The hypotenuse of a right angled triangle has its ends at [...]

16. Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point. 16. Find the direction in which a straight line must be drawn through [...]

15. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0 15. Find the distance of the line 4x + 7y + 5 = 0 from the point (1 2) along the line 2x – y = 0 October [...]