CBSE Guess > Papers > Important Questions > Class XI > 2013 > Mathematics > Mathematics By Mr. Sumit Luthra

CBSE CLASS XI

ASSIGNMENT ON CONIC SECTION

1. Find the area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) .
2. Find the equation of the circle which touches both the axes and whose radius is a.  
3. Find the centres of the circles x² + y² = 112x +4y = 1, x² + y² + 6x - 2y =1= 1  and x² + y² -12x +4y = 1.Check weather the centres are collinear or not.
4. The lines 2x- 3y =5 and 3x - 4y =7 are the diameters of a circle of area 154 square units .Find the equation of the circle.
5. Find the equation of the circle which touches x-axis and whose centre is (1, 2). 
6. If the radius of the circle x² + y² -18x +12y +k = 0 be 11, then Find k      
7. ABC is a triangle in which angle C is a right angle. If the coordinates of A and B be (–3, 4) and (3, –4) respectively, then Find the equation of the circumcircle of triangle ABC .
8. If the vertices of a triangle be (2, -2), (-1, -1) and (5, 2), then Find the equation of its circumcircle.  
9.  Find the equation of the circle passing through the origin and cutting intercepts of length 3 and 4 units from the positive axes.
10. Find the equation of the circle having centre (1, -2) and passing through the point of intersection of lines 3 x+ y = 143x+y=14.
11. Find the equation of the circle concentric with the circle x² + y² +8x +10y -7 = 0  and passing through the centre of the circle x² + y²- 4x - 6y= 0 .
12. A circle is concentric with the circle x² + y²- 6x +12y +15 = 0  and has area double of its area. The Find the equation of the circle.
13. Find the centre and radius of the circle 2x² + 2y = 0.
14. Find the equation of the circle touching x = 0, y=0 and x = 4.
15. Find the equation of a circle whose centre is origin and radius is equal to the distance between the lines x = 1 and x=-1.
16. Find the equation of the circle concentric with the circle x² + y²-4x-6y-3= 0 and touching y-axis.
17. Find the area of a circle whose centre is (h, k) and radius a.
18. Find the equation of circle whose diameter is the line joining the points (­–4, 3) and (12, –1).
19. Find the equation of the circle which passes through the points (3, -2) and (-2, 0) and centre lies on the line 2x-y=3.
20. Find the area of the circle in which a chord of length √2 makes an angle x/2 at the centre.
21. If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2,y), then Find the the value of x and y.
22. Find the equation of the circle in the first quadrant which touches each axis at a distance 5 from the origin .
23. Find the equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible.
24. Find the equation of the circumcircle of the triangle formed by the lines x=0, y=0, 2x+3y=5.
25. Find the equation of the circle whose diameter lies on 2x +3y =3 and 16x-y = 4 which passes through (4,6).
26. Find the area of the curve x² + y² = 2ax.
27. The centre of a circle is (2, –3) and the circumference is 10x. Then Find the equation of the circle.
28. For what value of k, the points (0, 0),(1, 3), (2, 4) and (k, 3) are con-cyclic.
29. For what value of k, the points (2k, 3k), (1, 0), (0,1) and (0,0) lie on a circle.
30. Check weather the point (1, 1) lies inside,outside or on  the circle x² + y²- x+y = 0 .
31. Find the equation of the circle with origin as centre passing the vertices of an equilateral triangle whose median is of length 3a.
32. A circle is inscribed in an equilateral triangle of side a, Find the area of any square inscribed in the circle.

Submitted By Mr. Sumit Luthra
About author: Pgt math,Mount Caremel school,N.D 76
Mobile:9891985899
Email: [email protected]