1. The circle with equation 2x^2 + 2y^2 - x = 0 has center (1/2, 0) and radius sqrt(3)/2. 2. The angle between the x-axis and the line joining the points (3, -1) and (4, -2) is the arctangent of 1/1 = 45 degrees. 3. If the sum to n terms of an AP is nP + 1/2n(n-1)Q, where P and Q are constants, the common difference is Q.

1. 1
Class – XI (Chapters 9, 10,11) Subject: Mathematics
1. Findthe centerand radiusof the circle 2x2
+2y2
-x=0
2. Find the angle between x-axis and the line joining the points (3,-1) and (4,-2)
3. If the sumto n termsof an A.P.if nP+1/2 n(n-1)Q,where Pand Q are constants,findthe commondifference.
4. The line throughthe points(h,3) and(4,1) intersectsthe line 7x-9y-19=0at rightangle.Findthe value of h.
5. Findthe sum to n termsof the series:
1
1×2
+
1
2×3
+
1
3×4
+ ⋯
6. Determine the equation of line through the point (-4, -3) and parallel to x – axis.
7. Findthe equationof the hyperbolawhere foci are (0, ±12) and the lengthof latusrectumis 36.
8. Findthe value of 𝜃 and p if the equationxcos𝜃 +ysin𝜃=pisthe normal form of the line √3x+y+2=0
9. If a(
1
𝑏
+
1
𝑐
) , b(
1
𝑐
+
1
𝑎
),c(
1
𝑎
+
1
𝑏
) are in A.P.prove thata, b, c are in A.P.
10. If S be the sum , Pthe productand R the sum of the reciprocalsof nterms of a G.P. Prove that: (
𝑺
𝑹
)
𝒏
= 𝑷 𝟐 .
11. Showthat the product of perpendicularsonthe line
𝒙
𝒂
𝒄𝒐𝒔 𝜽 +
𝒚
𝒃
𝒔𝒊𝒏 𝜽 = 𝟏fromthe points (±√𝒂 𝟐 − 𝒃 𝟐 ,𝟎) is b2
.
12. A rod of length12cm moveswithitsendsalwaystouchingthe coordinate axes.Determine the equationof locusof
PointP onrod, whichis3cm fromthe endin contact withx-axis.
13. If p and p' be the perpendicular from the origin upon the straight lines x secθ + y cosecθ = a and
x cosθ - y sinθ = a cos 2θ. Prove that 4p2
+p'2
= a2
.
14. A line is such that its segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5).
Obtainits equation
15. Referredtoitsprincipal axesasaxesof coordinatesfindthe equationof the hyperbolawhosefoci are at (𝟎, ± √ 𝟏𝟎)
and whichpassesthroughthe point(2,3).
16. Findthe equationof anellipse whose axes lie alongx- axisandwhichpassesthrough(4,3) and(6, 2).
17. Findthe equationof the circle whichpassesthroughthe points(7,1), (-2,4) and (5, 5). Findalsothe coordinatesof
itscentre and radius.
18. Findthe equationof a line drawnperpendiculartothe line
𝒙
𝟒
+
𝒚
𝟔
= 𝟏throughthe pointwhere it meets the y – axis.
19. Two lines passing through the point (2, 3) intersect each other at an angle of 60o
. If slope of one line is 2, find the
equation of the other line.
20. If a and b are the rootsof x2
– 3x + p = 0 and c , d are the roots x2
– 12x + q = 0, where a,b, c, d form a G.P.Prove
that (q+ p) : (q – p) = 17 : 15.
21. If
𝑎+𝑏𝑥
𝑎−𝑏𝑥
=
𝑏+𝑐𝑥
𝑏−𝑐𝑥
=
𝑐+𝑑𝑥
𝑐−𝑑𝑥
(𝑥 ≠ 0) , then show that a, b, c and d are in G.P.
22. The sum of first three of a G.P. is 16 and the sum of the next three terms is 128. Find the sum of n terms of the G.P.
23. Find the equation of the straight line which passes through the point (2, -3)and the point of intersection of the lines
x + y + 4 = 0 and 3x – y – 8 = 0.
24. Prove that the radii of the circles x2
+ y2
= 1, x2
+ y2
– 2x - 6y - 6 = 0 and x2
+ y2
– 4x - 12y - 9 = 0 are in A.P.
25. Find the equation of the circle concentric with the circle 2x2
+ 2y2
+ 8x + 12y – 39 = 0 and having its area equalto
16π square units.
26. If x = 1 + a + a2
+ a3
+ ............... ∞,where | 𝑎| < 1 and y = 1+ b + b2
+ b3
+ ............... ∞,where | 𝑏| < 1 . Prove that
1 + ab + a2
b2
+ ............... ∞ =
𝑥𝑦
𝑥+𝑦−1
.