Home
Class 12
MATHS
Area of the triangle formed by the line ...

Area of the triangle formed by the line `x+y=3` and the angle bisectors of the pairs of straight lines `x^2-y^2+2y=1` is
(a)`2sq units`
(b)`4sq units`
(c)`6sq units`
(d)`8sq units`

A

`2` sq units

B

`4` sq units

C

`6` sq units

D

`8` sq units

Text Solution

Verified by Experts

Given, `x^(2)-y^(2)+2y=1`
`impliesx^(2)=(y-1)^(2)`
`impliesx=y-1` and `x=-y+1`

From the graph, it is clear that equation of angle bisectors are
`y=1`
and `x=0`
`:.` Area of region bounded by `x+y=3`, `x=0`
and `y=1` is `Delta=(1)/(2)xx2xx2=2`sq. units
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the area of the triangle formed by the line x+y=3 and the angle bisectors of the pair of lines x^2-y^2+4y-4=0

The area enclosed by 2|x|+3|y|lt=6 is (a)3 sq. units (b) 4 sq. units (c)12 sq. units (d) 24 sq. units

The area of the quadrilateral formed by the tangents at the endpoint of the latus rectum to the ellipse (x^2)/9+(y^2)/5=1 is (A) 27/4 sq. unit (B) 9 sq. units (C) 27/2 sq. unit (D) 27 sq. unit

If the area of the triangle formed by the points (1,2) (2,3) and a,4) is 8 sq. units find a.

If the area of the triangle formed by the points (x,2x) ,(-2,6) and (3,1) is 5 square units then x=………….

The area bounded by the curves y=|x|-1a n dy=-|x|+1 is 1 sq. units (b) 2 sq. units 2sqrt(2) sq. units (d) 4 sq. units

The minimum area of the triangle formed by the tangent to (x^2)/(a^2)+(y^2)/(b^2)=1 and the coordinate axes is (a) a b sq. units (b) (a^2+b^2)/2s qdot""u n i t s (c) ((a+b)^2)/2s qdot""u n i t s (d) (a^2+a b+b^2)/3 sq. units

A rhombus is inscribed in the region common to the two circles x^2+y^2-4x-12=0 and x^2+y^2+4x-12=0 with two of its vertices on the line joining the centers of the circles. The are of the rhombus is (A) 8sqrt(3) sq.units (B) 4sqrt(3) sq.units (C) 6sqrt(3) sq.units (D) none of these

If the area of the triangle formed by the vertices (p,p),(5,6),(5,-2) is 32 sq. units. Find the value of p.