# Topic: Chapter 5: Two Dimensional Analytical Geometry II (Test 1)

Topic: Chapter 5: Two Dimensional Analytical Geometry II
Q.1
The equation of the circle passing through (1, 5) and (4,1) and touching y -axis is x2 + y2 − 5x − 6 y + 9 + λ (4x + 3y −19) = 0 where λ is equal to
A. 0, - 40/9
B. 0
C. 40/9
D. -40/9
Answer : Option A
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Q.2
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is
A. 4/3
B. 4/√3
C. 2√3
D. 3/2
Answer : Option C
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Q.3
The circle x2 + y2 = 4x + 8 y + 5 intersects the line 3x − 4 y = m at two distinct points if
A. 15 < m < 65
B. 35 < m < 85
C. -85 < m < -35
D. -35 < m < 15
Answer : Option D
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Q.4
The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point (2, 3)
A. 6/5
B. 5/3
C. 10/3
D. 3/5
Answer : Option C
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Q.5
The radius of the circle 3x2 + by2 + 4bx − 6by + b2 = 0 is
A. 1
B. 3
C. √10
D. √11
Answer : Option C
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Q.6
The centre of the circle inscribed in a square formed by the lines x2 − 8x −12 = 0 and  y2 −14 y + 45 = 0 is
A. (4, 7)
B. (7, 4)
C. (9, 4)
D. (4, 9)
Answer : Option A
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Q.7
The equation of the normal to the circle x2 + y2 − 2x − 2 y +1 = 0 which is parallel to the line 2x + 4 y = 3 is
A. x + 2 y = 3
B. x + 2 y + 3 = 0
C. 2 x + 4 y + 3 = 0
D. x - 2 y + 3 = 0
Answer : Option A
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Q.8
If P(x, y) be any point on 16x2 + 25 y2 = 400 with foci F1 (3, 0) and F2 (−3, 0) then PF1 + PF2 is
A. 8
B. 6
C. 10
D. 12
Answer : Option C
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Q.9
The radius of the circle passing through the point (6, 2) two of whose diameter are x + y = 6 and x + 2 y = 4 is
A. 10
B. 2√5
C. 6
D. 4
Answer : Option B
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Q.10
The area of quadrilateral formed with foci of the hyperbolas  is
A. 4(a2 + b2 )
B. 2(a2 + b2 )
C. a2 + b2
D. 1/2 (a2 + b2 )
Answer : Option B
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