alleryStart learning →Which line is the set of points as near to the origin as to (4, 0)?
- x = 2
- y = 2
- x = 4
- x + y = 4
Show answer and solution
Correct answer: A. x = 2
Setting x² + y² = (x - 4)² + y² gives 8x = 16, so x = 2, the perpendicular bisector of the segment.
AP EAMCET Coordinate Geometry: Locus — practice questions
Explore 42 free Coordinate Geometry: Locus questions in AP EAMCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Coordinate Geometry: Locus with Quill →Coordinate Geometry: Locus questions and exercises with answers
Showing questions 1–30 of 42.
Which line is the set of points as near to the origin as to (4, 0)?Read the answer and worked solution →Points P satisfy PA = PB with A(1, 2) and B(3, 4). What is the equation of this set?Read the answer and worked solution →Every point of a curve is as far from (2, 0) as from (0, 2). Its equation isRead the answer and worked solution →A point stays exactly 5 units from the origin. Which equation holds for it?Read the answer and worked solution →A point stays 3 units from (2, -1). Its locus has equationRead the answer and worked solution →A point moves so its distance from the x-axis is always 3. The locus isRead the answer and worked solution →The distance of P from the y-axis is double its distance from the x-axis. P lies onRead the answer and worked solution →Squares of a point's distances to (1, 0) and (-1, 0) add up to 10. It lies onRead the answer and worked solution →PA² exceeds PB² by 8, with A the origin and B(4, 0). P lies onRead the answer and worked solution →A parabola has focus (2, 0) and directrix x = -2. Give its equation.Read the answer and worked solution →A dish has focus (0, 3) and directrix y = -3. Which equation fits it?Read the answer and worked solution →Each point of a curve is as far from the origin as from the line x = -1. The curve isRead the answer and worked solution →Find the ellipse with foci (±3, 0) and focal distance sum 10.Read the answer and worked solution →A string of length 8 loops foci at (2, 0) and (-2, 0). The pencil tracesRead the answer and worked solution →Foci at (0, 4) and (0, -4) with focal sum 10 give the ellipseRead the answer and worked solution →Which hyperbola has foci (±5, 0) and focal difference 6 in size?Read the answer and worked solution →A hyperbola has foci (±5, 0) and transverse axis length 8. It isRead the answer and worked solution →Points at twice the distance from the origin as from (3, 0) lie onRead the answer and worked solution →P runs on x² + y² = 36 and A is (6, 0). The midpoint of PA moves onRead the answer and worked solution →P slides along x + y = 4 and O is the origin. The midpoint of OP tracesRead the answer and worked solution →A ladder of length 6 slides with its ends on the axes. Its midpoint tracesRead the answer and worked solution →A(-2, 0) and B(2, 0) are fixed. A point P sees AB at a right angle. P lies onRead the answer and worked solution →The area of triangle PAB is 8 with A(0, 0) and B(4, 0). The locus of P isRead the answer and worked solution →The locus of points equidistant from two intersecting lines isRead the answer and worked solution →All points with equal distances from the lines y = x and y = -x satisfyRead the answer and worked solution →Points where |x| and |y| agree, being equally far from both axes, lie onRead the answer and worked solution →Which pair of lines is traced by a point 2 units away from y = 1?Read the answer and worked solution →A point is double as far from the origin as from the x-axis. It lies onRead the answer and worked solution →A point sees the segment from (1, 2) to (5, 4) at a right angle. Its path isRead the answer and worked solution →The Latin word from which "locus" comes meansRead the answer and worked solution →
Worked practice questions
Points P satisfy PA = PB with A(1, 2) and B(3, 4). What is the equation of this set?
- x - y = 5
- x + y = 5
- x + y = 7
- x - y = -1
Show answer and solution
Correct answer: B. x + y = 5
Equating squared distances gives 4x + 4y = 20, that is x + y = 5, the perpendicular bisector of the join.
Every point of a curve is as far from (2, 0) as from (0, 2). Its equation is
- x + y = 2
- x = 2
- y = 2
- y = x
Show answer and solution
Correct answer: D. y = x
(x - 2)² + y² = x² + (y - 2)² simplifies to -4x = -4y, so the path is y = x.
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