Analytic Geometry and Ans

CET11 Mathematics Question Bank – Straight Lines, Pair of Lines & Circles A straight line through the point A  3, 4  is such that its intercept between the axes is bisected at
A . It’s equation is

1.

(a) 4 x  3 y  24 Ans: a

(b) 3x  4 y  25

(c) x  y  7

(d) 3x  4 y  7  0

Sol: By formula required equation is given by

x y   2  4 x  3 y  24 3 4
2. The equation of the line which is the perpendicular bisector of the line joining the points  3, 5 and  9,3 is (a) 4 x  3 y  14  0 Ans: d Sol: A   3, 5 B   9,3 Midpoint of AB   6, 1 . Slope of AB  Slope of perpendicular line  (b) 3x  4 y  14  0 (c) 3x  4 y  14  0 (d) 3x  4 y  14  0

8 4  6 3

3 4 3  x  6 4

Equation of required line y  1  i.e., 3.
3x  4 y  14  0

The radius of the circle 16x2  16y 2  8x  32y  239  0 is (a) 32 Ans: c (b) 16 (c) 4 (d) none of these

4.

The equation of the circle with centres at (2, -3) and touching y  axis is (a) x2  y 2  4 x  6 y  4  0 (c) x2  y 2  4 x  6 y  9  0 Ans: c (b) x2  y 2  4 x  6 y  4  0 (d) none of these

5.

The equation of the line whose intercepts on x -axis and y -axis are 3 and 4 is (a) 4 x  3 y  12  0 Ans: b Sol: Points on required line  3,0  Equation of line (b) 4 x  3 y  12  0 (c) 4 x  3 y  12  0 (d) x  y  1  0

 0, 4

x y   1  4 x  3 y  12  0 3 4
3 is given by, 2

6.

The equation of the line whose y intercept is 2 and slope is

1

CET11 Mathematics Question Bank – Straight Lines, Pair of Lines & Circles (a) 2 x  3 y  4  0 x Ans: c Sol: Equation of line y  mx  c  y  (b) 3x  2 y  4  0 (c) 3x  2 y  4  0 (d) 3x  2 y  4  0

3 x2 2

 3x  2 y  4  0

7.

The center of the circle 36x2  36y 2  24x  36y  23  0 is (a) (12, -18) Ans: c (b)   , 
 1 1  3 2

(c)  , 

1 3

1 2

(d) (  , )

1 3

1 2

8.

The equation of the circle of area 4 lying in the first quadrant