Coordinate Geometry CAT Previous Year Questions with Answer PDF

So, every point on the line y = 2x − 7 where x ≤ 5 satisfies the given condition.
We are to find the area enclosed by the y-axis, x = 5 and the lines of |x−y|−|x−5|=2 .
Because the area we are interested is bounded by x = 0 (y-axis) and x = 5, 0 ≤ x ≤ 5.
So, we’ll only be concerned about Case III and Case IV.
A rough sketch of the bounded region looks like…

The line y = 2x – 7 touches x = 0 and x = 5 at (0, -7) and (5, 3) respectively.

The graph of | x | - y ≤ 1, y ≥ 0 and y ≤ 1 is as follows:

Area of ABCD = Area of EFCD - Area of EAD - Area of BFC
= 
= 
= 4 - 1 = 3 Square units.

Let us first consider travelling from (1,1) to (4, 6)
This means, Travelling from 1 to 4 units in the x axis → 3 horizontal movements (h h h)
And travelling from 1 to 6 units in the y axis -> 5 vertical movements (v v v v v)
No matter how we proceed, reaching from (1,1) to (4,6) requires 5 vertical movements and 3 horizontal movements.
So, Number of paths to travel from (1,1) to (4,6) = Number of ways of arranging (h h h v v v v v)
Number of ways of arranging (h h h v v v v v) = 
Similarly, travelling from (4, 6) to (8, 10) requires 4 horizontal movements and 4 vertical movements
Number of ways of arranging (h h h h v v v v) = 
Total number of paths =   x  =  x  = 3920

We know that the equation of the straight line is 3x + 5y = 45

The intercepts are (15,0) and (0,9) respectively
Since it's a right-angled triangle, we know that Circumradius (R) = 
Circumradius = = 
We know that  is approximately equal to 6
So, from trial and error to find the closest number, we find that the value of Circumradius is very close to 9
So, the integer closest to L = 9

Construct the given data on a rough graph.
Required area = Sum of area of two smaller triangles [ (-2,0) (-1,1) (-1,-1) and (2,0) (1,-1) (1,1) ]
Required area = 2 x 1/2 x base x height
Required area = 1 x 2 = 2 Sq units