Mathematics

Mathematics 

Q-1 The radius of 5 (x2 + y2) – 5 (x + y) + 10 = 0 is
(a) Ö6/7
(b) Ö5/2
(c) Ö7/9
(d) Ö9/16

Q-2 The radical plane of x2 + y2 + 2x + 6y + 9 = 0 & x2 + y2 + 6x + 9y – 8 = 0 is
(a) 4x + 5y – 18 = 0
(b) 4x + 5y – 17 = 0
(c) 4x + 8y + 19 = 0
(d) None

Q-3 The center of circle x2 + y2 + 2u1 x + 2v1 y + d = 0 is
(a) (u1 , v1)
(b) ( – u1, – v)
(c) (– u1/2, – v1/2)
(d) None

Q-4 In y2 = 2x, the vertex is
(a) (0, 1)
(b) (0, 2)
(c) (0, 0)
(d) None

Q-5 In ( x – 5)2 + ( y – 3)2 = 5
Find the center & radius of a circle.
(a) (5, 3) & Ö5
(b) (5, 4), 5
(c) (5, 2), 6
(d) None

Q-6 In eq. of circle coefficient of x2 is equal to y2 & it should be equal to
(a) 2
(b) 1
(c) 3
(d) 4

Q-7 The eq. of tangent to the circle x2 + y2 = 5 at (5, 3) is
(a) 5x + 9y = 10
(b) 5x + 3y = 5
(c) 5x + 9y = 4
(d) None

Q-8 In the circle x2 + y2 + 2xy + 5z + c = 0, the centre is
(a) (0, 0)
(b) (1, 1)
(c) It is not a circle
(d) (4, 3)

Q-9 In order to find pt. of intersection two line should be
(a) Intersecting
(b) Parallel
(c) a and b
(c) None

Q-10 When distance between centre of two circle is equal to sum of their radius, then in this case two circle touch each other
(a) Internally
(b) Externally
(c) Not touch
(d) None

Q-11 The eq. of circle with end pt. of diameter is (5, 2) & (1, 5) is
(a) x2 + y2 – 6x + 7y – 10 = 0
(b) x2 + y2 – 6x – 7y + 10 = 0
(c) x2 + y2 + 6x + 7y – 11 = 0
(d) x2 + y2 – 6x + 7y – 11 = 0

Q-12 If we want to find radical plane, then how many circle we held
(a) 2
(b) 3
(c) 5
(d) 9

Q-13 If in a equation Ax2 + By2 + 2Hxy + 2Gx + 2Fy + c = 0
B2 – AB = 0, Then is a
(a) Ellipse
(b) Parabola
(c) Hyperbola
(d) None

Q-14 In x2/a2 + y2/b2 = 1, then value of major axis is
(a) 2a
(b) 2b
(c) 2d
(d) None

Q-15 In x2/a2 + y2/b2 = 1, then value of minor axis is
(a) 2a
(b) 2b
(c) 2e
(d) None

Q-16 In x2/25 + y2/16 = 1, the latus rectum is
(a) 32/5
(b) 16/14
(c) 16/9
(d) None

Q-17 In y2 = 4ax, the eq. of axis is
(a) x = 0
(b) y = 0
(c) x = y= 0
(d) None

Q-18 If Ratio of distance of any pt. on conic to focus & directrix is 1, then it is
(a) Parabola
(b) Ellipse
(c) Hyperbola
(d) None

Q-19 If a = b in x2/a2 – y2/b2 = 1, then it is
(a) Rectangle hyperbola
(b) Hyperbola
(c) Ellipse
(d) None

Q-20 For rectangle hyperbola, the value of l is
(a) Ö2
(b) Ö3
(c) Ö14
(d) Ö5

Q-21 What is parametric form of x2 + y2 = r 2 ?
(a) x = r cos Ө, y = r sin Ө
(b) x = cos Ө, y = sin
(c) x = r2 cos Ө, y = r2 sin Ө
(d) None

Q-22 Find the eq. of axis of (x + 1)2/52 + (y + 1)2 /32 = 1
(a) y = 0
(b) y = 1
(c) y = 3
(d) y = 5

Q-23 What is the focus of parabola y2 = 8x ?
(a) (2,0)
(b) (3,0)
(c) (4,0)
(d) (5,1)

Q-24 What is the focus of a parabola ?
Y2 = – 36x
(a) (0, – 9)
(b) (0,9)
(c) (0,5)
(d) (0,4)

Q-25 What is focus of a parabola x2 = 36y ?
(a) (0,4)
(b)(0,9)
(c)(0,5)
(d) None

Answers:

1(b) Ö5/2
2(b) 4x + 5y – 17 = 0
3(b) ( – u1, – v1)
4(c) (0, 0)
5(a) (5, 3) & Ö5
6(b) 1
7(b) 5x + 3y = 5
8(c) It is not a circle
9(a) Intersecting
10(b) Externally
11(b) x2 + y2 – 6x – 7y + 10 = 0
12(a) 2
13 (b)Parabola
14(a) 2a
15(b) 2b
16(a) 32/5
17(b) y = 0
18(a) Parabola
19(a) Rectangle hyperbola
20(a) Ö2
21(a) x = r cos Ө, y = r sin Ө
22(a) y = 0
23(a) (2,0)
24(a)(0, – 9)
25(b)(0,9)

Reason:

1 (x2 + y2) – 5 (x + y) + 10 = 0
First of all divide it by 5 because coefficient of x2 & y2 should be 1
(x2 + y2) – x – y – 2 = 0
( ½, 1/2), d = – 2
radius = Ö(1/2)2 + (1/2)2 + 2
Ö1/4 + ¼ +2
Ö2/4 + 2
Ö1/2 + 2 = Ö 5/2
2 Let S1 = x2 + y2 + 2x + 6y + 9 = 0
S2 = x2 + y2 + 6x + 6y + 9 = 0
Eq. of radical plane is
S1 – S2 = 0
– 4x – 5y + 17 = 0
4x + 5y – 17 = 0
7 Equation of Tangent at (x1, y1)
xy1 + yy1 = 5
But at pt. (5, 3) it is
x(5) + y(3) = 5
5x + 3y = 5
8 It is not a circle because in circle there is not any term which contain xy etc
11 Equation of circle in diameter form is
(x – x1) (x – x2) + (y – y1) (y – y2) = 0
(x – 5) (x – 1) + (y – 2) (y – 5) = 0
x2 – x – 5x +5 + y2 – 5y – 2y + 5 = 0
x2 – 6x + 5 + y2 – 7y + 5 = 0
x2 + y2 – 6x – 7y + 10 = 0
16 Latus rectum is 2b2/a
By x2/25 + y2/16 = 1
a2 = 25, b2 = 16, a = 5, b = 4
Latus rectum = 2b2/a = 2(16)/5 = 32/5
22 For x2/a2 + y2/b2 = 1, the eq. of axis in y = 0
23 Compare y2 = 8x
With y2 = –4ax
4a = 8, a = 2
F (a, 0), i.e F (2, 0)
24 Compare y2 = – 36x
With y2 = –4ax
4ax = 36, a = 9
F (–a, 0) , F (–9, 0)