22.1 Locus From Common Conditions
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1 .5 of 52 Locus From ommon onditions 22.1 Locus From ommon onditions Example 1 1. In the figure, EG is a square with sides of 2 cm. iagonals E and G intersect at K.,, F and H are the midpoints of, E, EG and G respectively. If a moving point keeps a fixed distance of 1 cm from K, which of the following is the locus of?. Square EG. Square FH. circle passing through,, E and G. circle passing through,, F and H K H G F E 2. The length and the width of a rectangular basketball court are 28 m and 15 m respectively. The running path of Jason maintains a fixed distance of 5 m from the court. Which of the following is the locus of? In the figure, is a line segment of 5 cm long. is a moving point such that the area of Δ is 10 cm 2. 5 cm Which of the following is the locus of?.. 2 cm Locus of 2 cm 2 cm Locus of Locus of.. Locus of Locus of Locus of
2 Locus From ommon onditions.6 of The figure shows an equilateral triangle. Which of the following lines may represent the locus of a point such that =?.... one of the above 5. In the figure, is a square and its diagonals intersect at E. is a moving point inside or on the square such that is equidistant from and. The locus of is. E.... E In the figure, is a rectangle. is the mid-point of and = = =. is a moving point inside the rectangle and is equidistant from line segment and point. Which of the following is the locus of?.. Locus of Locus of.. Locus of Locus of [lass ractice 1:.1]
3 .7 of 52 Locus From ommon onditions Example 2 1. moving point keeps a fixed distance d from a fixed point. The locus of is. a circle.. a straight line.. a parabola.. a pair of parallel lines. 2. Which of the following description about locus X and locus Y are correct? Locus X: Locus Y: The locus of a moving point X which is equidistant from two points and The locus of a moving point Y which is equidistant from two intersecting lines. Locus X Locus Y. ngle isector erpendicular isector. erpendicular isector ngle isector. ngle isector ngle isector. erpendicular isector erpendicular isector [WY_5a_1112_#15] 3. moving point maintains an equal distance from a point and a line. Which of the following does the locus of belong to?. circle. straight line. pair of straight lines. parabola 4. The equation of the straight line L is 3x 4y = 5. If is a moving point in the rectangular coordinate plane such that the perpendicular distance from to L is equal to 5 units, then the locus of is a. circle.. parabola.. square.. pair of parallel lines. [WY_5b_1314_#14] 5. The equations of the straight lines L 1 and L 2 are y = 2x 6 and 4x 2y = 15 respectively. If is a moving point in the rectangular coordinate plane such that the perpendicular distance from to L 1 is equal to the perpendicular distance from to L 2, then the locus of is. a square.. parabola.. a straight line.. pair of parallel lines. [HKE_S6_3_#26] [lass ractice 2:.8]
4 Sketch and escribe Locus.8 of Sketch and escribe Locus Example 3 1. In the figure, point moves inside such that =. Sketch and describe the locus of. 2. moving point forms such that maintains a fixed area of 2. Sketch and describe the locus of. 3. The figure shows a rhombus. is a moving point inside or on the rhombus. Sketch and describe the locus of which maintains the same distance from and.
5 .9 of 52 Sketch and escribe Locus 4. The figure shows a square wooden board of side 15 cm and a circular ring with diameter 10 cm. is the centre of the ring. The ring is outside the board and rolls along the sides of the board. Sketch and the locus of. 5. In the figure, is an equilateral triangle of side 5 cm. point moves such that it keeps a distance of 1 cm from the nearest point of. Sketch the locus of. 5 cm 6. In the figure, QRS is a rectangular house with QR = and RS = 8 cm. dog is tied to corner Q by a string of 6 cm. ssuming the string is always taut, sketch and describe the locus of the dog when it runs. [lass ractice 3:.12]
6 Equations of Locus.10 of Equations of Locus Example 4 1. It is given that a moving point is equidistant from (7, 8) and (5, 1). (a) escribe the locus of. (b) Find the equation of the locus of. y (7, 8) O (5, 1) x 2. moving point maintains a fixed distance o from Q(3, 5). The locus of passes through (1, 2) (a) Find the equation of the locus of. (b) escribe the locus of. 3. (5, 3) and (3, 1) are two points in a rectangular coordinate plane. point moves such that = 2. Find the equation of the locus of. [lass ractice 4:.17]
7 .17 of 52 Exam Questions 22.5 Exam Questions Example ( 2, 1) and (3, 5) are two points in a rectangular coordinate plane. is rotated anti-clockwise about the origin O through 270 to. is reflected in the x-axis to. (a) Find the coordinates of and. (b) moving point Q maintains Q = Q with and. Find the equation of the locus of Q. [lass ractice 10:.41]
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