Worksheets12 MATHS UNIT 5 BOOK BACK ONE MARK ONLINE TEST
Total questions: 26
Worksheet time: 13mins
1. 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
0,-40/9
0
40/9
-40/9
2. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is
3. The circle x 2 + y 2 = 4 x + 8 y + 5 intersects the line 3 x − 4 y = m at two distinct points if
(1) 15 < m < 65
(2) 35 < m < 85
(3) − 85 < m < − 35
(4) − 35 < m < 15
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 ) .
6/5
5/3
10/3
3/5
5. The radius of the circle 3 x 2+ by2 + 4 bx − 6 by + b2 = 0 is
1
3
6. 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
(4,7)
(7,4)
(9,4)
(4,9)
7. 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
x + 2 y = 3
x + 2 y + 3 = 0
2 x + 4 y + 3 = 0
x − 2 y + 3 = 0
8. 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
8
6
10
12
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
10
6
4
4(a2+b2)
2(a2+b2)
a2+b2
1/2(a2+b2)
11. If the normals of the parabola y 2 = 4 x drawn at the end points of its latus rectum are tangents to the circle ( x − 3 ) 2 + ( y + 2 ) 2 = r 2 , then the value of r 2 is
2
3
1
4
12. If x + y = k is a normal to the parabola y 2 = 12 x , then the value of k is
3
-1
1
9
x 2 + y 2 − 6 y − 7 = 0
x 2 + y 2 − 6 y + 7 = 0
x 2 + y 2 − 6 y − 5 = 0
x 2 + y 2 − 6 y + 5 = 0
16. Let C be the circle with centre at ( 1 , 1 ) and radius = 1. If T is the circle centered at ( 0 , y )
passing through the origin and touching the circle C externally, then the radius of T is equal
1/2
1/4
17. Consider an ellipse whose centre is of the origin and its major axis is along x-axis. If its eccentrcity is 3/5 and the distance between its foci is 6, then the area of the quadrilateral inscribed in the ellipse with diagonals as major and minor axis of the ellipse is
8
32
80
40
2ab
ab
a/b
19. An ellipse has OB as semi minor axes, F and F ′ its foci and the angle FBF ′ is a right angle.Then the eccentricity of the ellipse is
1/2
1/4
1/3
21. If the two tangents drawn from a point P to the parabola y 2 = 4 x are at right angles then the
locus of P is
2 x + 1 = 0
x = −1
2 x − 1 = 0
x = 1
22. The circle passing through ( 1 , - 2 ) and touching the axis of x at ( 3 , 0 ) passing through the point
( -5 , 2 )
( 2 , - 5 )
( 5 , - 2 )
( -2 , 5 )
a parabola
a hyperbola
an ellipse
a circle
2
4
0
-2
25. If the coordinates at one end of a diameter of the circle x 2 + y 2 − 8 x − 4 y + c = 0 are ( 11 , 2 ) ,
the coordinates of the other end are
( -5 , 2 )
( -3, 2)
( 5 , - 2 )
( -2 , 5 )
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