Home
Class 12
MATHS
The maximum area of the convex polygon f...

The maximum area of the convex polygon formed by joining the points `A(0,0),B(2t^2,0),C(18,2),D((8)/(r^2),4)` and `E(0,2)` where `tinR-{0}` and interior angle at vertex B is greater than or equal to `90^@`

Text Solution

Verified by Experts

The correct Answer is:
54

Slope of `BC =(2-0)/(18-2t^2)ge0`
`rArr18-2t^2ge0`
`rArrt^2-9le0rArrtin[-3,3]`
Now, area of quadrilateral
=Area of trapezium `ABCE+`Area of triangle `CDE `
` (1)/(2) (2t^2+18)xx2+(1)/(2)xx18xx2`
`36+2t^2 le 54`
So, the required maximum area is 54 sq.units.
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise JEE Main|6 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Matrix match type|4 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the lines joining the points (0,0) (2,3) and (2,-2),(3,5).

State which of the following is equal to the area of the traingle formed by joining the points (0,4) , (0,0) and (-6,0) ?

Consider the points A(0, 0, 0), B(5, 0, 0), C(3, 0, 4) and D(0, 4, 3). The points A, B, C and D are-

Calculating direction ratios show that the triangle formed by joining the points (2, 3, 1), (-2, 2, 0) and (0, 1, -1) in right-angled.

Let's plot the points A (4,0), B(0,6), C (2,5), D(7,1) E (?, 5) and F(?,5) on a graph sheet.

( c) Find the area of the quadrilateral formed by the four points (4,3),(2,5),(0,2) and (2,0) successively.

The points (-a,-b).(0,0),(a,b) and (a^2, ab) are

(a , 2b ) divides the line segment joining by the points (3a,0),(0,3b) in the ratio-

C is a point on the line-segment joining the points A (2,-3,4) and B(8, 0,10) if the y-coordinate of C is (-2,) then its z-coordinate will be-

Find the coordiantes of the point in the xy-plane which is equiistant from the points A ( 0 , 0 , 1) , B ( 2 , 0 , 3) and C ( 0 , 3 , 2) .