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14. A point P moves so that its distance form the origin is always twice its distance form the point (1. 4). The equation of the locus of P is: A. x* + y + 4x + 16y – 34 = 0 B. 3x² + 3y – 8x – 32y+ 68 = 0 C. 3x² + 3y + 2x+ 8y – 17= 0 D. x² + y + 2x + 8y + 17= 0

14. A point P moves so that its distance form the origin is always twice its distance form the point (1. 4). The equation of the locus of P is: A. x* + y + 4x + 16y – 34 = 0 B. 3x² + 3y – 8x – 32y+ 68 = 0 C. 3x² + 3y + 2x+ 8y – 17= 0 D. x² + y + 2x + 8y + 17= 0

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve all Q14, 15, 16 explaining detailly each step

14. A point P moves so that its distance form the origin is always twice its distance form the point (1, 4). The equation of the locus of P is: A. x + y + 4x+ 16y – 34 = 0 B. 3x+ 3y – 8x – 32y + 68 = 0 C. 3x + 3y + 2x + 8y – 17= 0 D. x+ y + 2x + 8y + 17 = () 2 %3D | - 15. A point p moves so that it is at a constant distance of 5 units from the line 4x - 3y = 1. The possible set of positions of p is defined by the equațion: A. 4x – 3y = 26 and 4x – 3y = 24 B. 4x + 3y = 2 and 4x + 3y = 24 C. 4x + 3y = 26 and 4x - 3y + 24 = 0 %3D %3D %3D %3D D. 4x – 3y – 26 = 0 and 4x – 3y+ 24 = 0 %3D | 16. The points M (-1, 0), N (1,0) and P (x, y) are such that angle MPN is right angles. The equation of the locus of P is: 2 A. x + y - 2x - 4y – 4= 0 B. x+ y - 8x +1 = 0 C. x² + y- 1= 0 D. 2x + 2y – 20x – 3 = 0 | 15.The equation of a circle with center (-1, 2) and radius 3 is A. x+ y - 2x - 4y – 4 = 0 B. x² + y² + 2x – 4y - 4 = 0 C. x + y-x + 2y –9 = 0 16. The equation of the circle passing through the point (2, 7) with centre at (1, 3) is A. (x – 2)² + (y – 7)² = 17 C. (x – 1)² + (y – 3)² = 17 17.The equation of a circle of a circle with the points (-2, 2) and (3, 1) as ends of a diameter is: A. x + y - x - 3y – 4 = 0 B. x² + y² + x – y + 1 = 0 C. x + y – 2x + 3y – 5 = 0 D. x + y + 5x- 3y - 4 0 18. A circle with centre at point (3,4) touches the x-axis. Find the equation of the circle D. x + y + 2x - 4y +2 = 0 %3D %3D B. (x + 1)² + (y + 3)² = 17 D. (x - 3)2 + (y – 1)2 = 17 | B. (x – 4)2 + (y – 3)² = 25 D. (x- 3)2 + (y - 4)2 = 9 A. (x – 3)² + (y – 4)² = 25 C. (x – 3)2 + (3y – 4)² = 16 19. y =x is tangent to the circle S, y = 3x passes through the center (p, q) of S. the radius of the circle S is given by %3D D. 2q A. r = 3p B. r = 3q + p C.r= v2p 20.The circle S with center (p, q) passes through the points (1, 1) and (2, 3). If a segment of the line y = x+ 2 is a diameter of S the value of P is: А. 3 В. 2 С. 1 D. 2 21. An equation of a circle passing through the points (2, 1) and (-2, –1) as end points of a diameter is A. x2 + y? - 2x – 4y - 5 = 0 C. x2 + y2 – 4x + 2y + 5 = 0 22. The line y = 3x – 5 is a tangent to the circle x + y = 2ax = 0, The possible values of 'a' are B. x2 + y2 - 5 = 0 D. x² + y? – 4x – 2y – 5 = 0 %3D %3D | %3D %3D given by the equation A. 10a - 3a + 5 = 0 B. 91a+ 30a -25 = 0 C. a+ 30a + 25 = 0 D. a + 30a - 25=0 %3D 23. The line 3x - 4y + 14 is a tangent to the circle
Transcribed Image Text:14. A point P moves so that its distance form the origin is always twice its distance form the point (1, 4). The equation of the locus of P is: A. x + y + 4x+ 16y – 34 = 0 B. 3x+ 3y – 8x – 32y + 68 = 0 C. 3x + 3y + 2x + 8y – 17= 0 D. x+ y + 2x + 8y + 17 = () 2 %3D | - 15. A point p moves so that it is at a constant distance of 5 units from the line 4x - 3y = 1. The possible set of positions of p is defined by the equațion: A. 4x – 3y = 26 and 4x – 3y = 24 B. 4x + 3y = 2 and 4x + 3y = 24 C. 4x + 3y = 26 and 4x - 3y + 24 = 0 %3D %3D %3D %3D D. 4x – 3y – 26 = 0 and 4x – 3y+ 24 = 0 %3D | 16. The points M (-1, 0), N (1,0) and P (x, y) are such that angle MPN is right angles. The equation of the locus of P is: 2 A. x + y - 2x - 4y – 4= 0 B. x+ y - 8x +1 = 0 C. x² + y- 1= 0 D. 2x + 2y – 20x – 3 = 0 | 15.The equation of a circle with center (-1, 2) and radius 3 is A. x+ y - 2x - 4y – 4 = 0 B. x² + y² + 2x – 4y - 4 = 0 C. x + y-x + 2y –9 = 0 16. The equation of the circle passing through the point (2, 7) with centre at (1, 3) is A. (x – 2)² + (y – 7)² = 17 C. (x – 1)² + (y – 3)² = 17 17.The equation of a circle of a circle with the points (-2, 2) and (3, 1) as ends of a diameter is: A. x + y - x - 3y – 4 = 0 B. x² + y² + x – y + 1 = 0 C. x + y – 2x + 3y – 5 = 0 D. x + y + 5x- 3y - 4 0 18. A circle with centre at point (3,4) touches the x-axis. Find the equation of the circle D. x + y + 2x - 4y +2 = 0 %3D %3D B. (x + 1)² + (y + 3)² = 17 D. (x - 3)2 + (y – 1)2 = 17 | B. (x – 4)2 + (y – 3)² = 25 D. (x- 3)2 + (y - 4)2 = 9 A. (x – 3)² + (y – 4)² = 25 C. (x – 3)2 + (3y – 4)² = 16 19. y =x is tangent to the circle S, y = 3x passes through the center (p, q) of S. the radius of the circle S is given by %3D D. 2q A. r = 3p B. r = 3q + p C.r= v2p 20.The circle S with center (p, q) passes through the points (1, 1) and (2, 3). If a segment of the line y = x+ 2 is a diameter of S the value of P is: А. 3 В. 2 С. 1 D. 2 21. An equation of a circle passing through the points (2, 1) and (-2, –1) as end points of a diameter is A. x2 + y? - 2x – 4y - 5 = 0 C. x2 + y2 – 4x + 2y + 5 = 0 22. The line y = 3x – 5 is a tangent to the circle x + y = 2ax = 0, The possible values of 'a' are B. x2 + y2 - 5 = 0 D. x² + y? – 4x – 2y – 5 = 0 %3D %3D | %3D %3D given by the equation A. 10a - 3a + 5 = 0 B. 91a+ 30a -25 = 0 C. a+ 30a + 25 = 0 D. a + 30a - 25=0 %3D 23. The line 3x - 4y + 14 is a tangent to the circle
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