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 B. (x + 1)? + (y + 3)? = 17 D. (x – 3)² + (y – 1)² = 17
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 B. (x + 1)? + (y + 3)? = 17 D. (x – 3)² + (y – 1)² = 17
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Solve all Q22, 16, 17 explaining detailly each step
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
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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
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D. 4x – 3y – 26 = 0 and 4x – 3y+ 24 = 0
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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
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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
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B. (x + 1)² + (y + 3)² = 17
D. (x - 3)2 + (y – 1)2 = 17
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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
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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
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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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