Coordinate Geometry (Railway Maths)

Total Questions: 57

41. The measure of the angle between the graph of linear equation 35x - 35y + 15 = 0 and the x-axis is: [RRB NTPC 05/04/2021 (Evening)]

Correct Answer: (d) 45°
Solution:

42. The chord of contact of tangents drawn from a point on the circle x² + y² = a² to the circle x² + y² = b² touches the circle x² + y² = c² such that bᵐ = aⁿcᵖ, where m, n, p ∈ N. Find the value of m + n + p + 10. [RRB NTPC 07/04/2021 (Morning)]

Correct Answer: (c) 14
Solution:

43. A circle has a radius of 3 units and its centre lies on the line y = x - 1. Find the equation of the circle if it passes through point (7, 3). [RRB NTPC 07/04/2021 (Morning)]

Correct Answer: (b) x² + y² - 8x - 6y + 16 = 0
Solution:

44. Find the length of the tangent from any point on the circle x² + y² + 2011x + 2012y + 2013 = 0 to the circle x² + y² + 2011x + 2012y + 2014 = 0. [RRB NTPC 07/04/2021 (Morning)]

Correct Answer: (d) No common tangent can be drawn.
Solution:

45. If a point (1, 2) is translated 2 units through the positive direction of x-axis and then the tangents drawn from the point to the circle x² + y² = 9, find the angle between the tangents. [RRB NTPC 07/04/2021 (Morning)]

Correct Answer: (c) 2tan⁻¹(3/2)
Solution:

46. In a parallelogram PQRS, P= (- 1, - 1) , Q = (8, 0) and R = (7, 5). What are the coordinates of ‘S’ ? [RRB NTPC 23/07/2021 (Evening) ]

Correct Answer: (b) (- 2 , 4)
Solution:

47. Find the length of the tangent from the point (2, 3) to the circle x² + y² = 4. [RRB NTPC 23/07/2021 (Evening)]

Correct Answer: (a) 3
Solution:

48. The equation of a line which passes through a point (1, 5) and perpendicular to the line x - y = 5, is: [RRB NTPC 24/07/2021 (Morning)]

Correct Answer: (b) x + y = 6
Solution:

49. ΔABC is a triangle whose vertices are A(0, 0), B (a, 5) and C(-5, 5). If the triangle is right-angled at A, then find the value of a. [RRB NTPC 26/07/2021 (Morning)]

Correct Answer: (b) 5
Solution:

50. Find the number of points on the x - axis that are at a distance of ‘c’ units (c < 3) from the point (2 , 3). [RRB NTPC 26/07/2021 (Morning) ]

Correct Answer: (a) 0
Solution: