The equation of the circle
passing through (1, 5) and (4,1) and touching *y *-axis is *x*^{2 }+
*y*^{2 }− 5*x *− 6 *y *+ 9 + *λ *(4*x *+ 3*y
*−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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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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The circle *x*^{2 }+
*y*^{2 }= 4*x *+ 8 *y *+ 5 intersects the line 3*x *−
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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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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The radius of the circle 3*x*^{2
}+ *by*^{2 }+ 4*bx *− 6*by *+ *b*^{2 }=
0 is

**A. ** 1

**B. ** 3

**C. ** √10

**D. ** √11

**Answer : ****Option C**

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The centre of the circle
inscribed in a square formed by the lines *x*^{2 }− 8*x *−12
= 0 and *y*^{2 }−14 *y *+ 45 = 0 is

**A. ** (4, 7)

**B. ** (7, 4)

**C. ** (9, 4)

**D. ** (4, 9)

**Answer : ****Option A**

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The equation of the normal
to the circle *x*^{2 }+ *y*^{2 }− 2*x *− 2 *y *+1
= 0 which is parallel to the line 2*x *+ 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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If *P*(*x*, *y*)
be any point on 16*x*^{2 }+ 25 *y*^{2 }= 400 with
foci *F*_{1 }(3, 0) and *F*_{2 }(−3, 0) then *PF*_{1
}+ *PF*_{2} is

**A. ** 8

**B. ** 6

**C. ** 10

**D. ** 12

**Answer : ****Option C**

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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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The area of quadrilateral
formed with foci of the hyperbolas is

**A. ** 4(*a*^{2} + b^{2} )

**B. ** 2(*a*2 + b^{2} )

**C. ** *a*^{2} + b^{2}

**D. ** 1/2 (*a*^{2} + b^{2} )

**Answer : ****Option B**

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