A rectangle `A B C D` has its side `A B` parallel to line `y=x ,` and vertices `A ,Ba n dD` lie on `y=1,x=2,` and `x=-2,` respectively. The locus of vertex `C` is (a)`x=5` (b) `x-y=5` (c)`y=5` (d) `x+y=5`

A rectangle PQRS has its side PQ parallel to the line y= mx and vertices P, Q , and S on the lines y= a, x=b ,and x= - b , respectively. Find the locus of the vertex R .

In a triangle A B C , the bisectors of angles Ba n dC lies along the lines x=ya n dy=0. If A is (1,2) , then the equation of line B C is (a) 2x+y=1 (b) 3x-y=5 (c) x-2y=3 (d) x+3y=1

Triangle A B C with A B=13 ,B C=5, and A C=12 slides on the coordinates axes with Aa n dB on the positive x-axis and positive y-axis respectively. The locus of vertex C is a line 12 x-k y=0. Then the value of k is_____________

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

Given A-=(1,1) and A B is any line through it cutting the x-axis at Bdot If A C is perpendicular to A B and meets the y-axis in C , then the equation of the locus of midpoint P of B C is (a) x+y=1 (b) x+y=2 (c) x+y=2x y (d) 2x+2y=1

The equations of two equal sides A Ba n dA C of an isosceles triangle A B C are x+y=5 and 7x-y=3 , respectively. Then the equation of side B C if a r( A B C)=5u n i t^2 is x-3y+1=0 (b) x-3y-21=0 3x+y+2=0 (d) 3x+y-12=0

If (-4,0) and (1,-1) are two vertices of a triangle of area 4s qdotu n i t s , then its third vertex lies on y=x (b) 5x+y+12=0 (c) x+5y-4=0 (d) x+5y+12=0

In triangle A B C , the equation of the right bisectors of the sides A B and A C are x+y=0 and y-x=0 , respectively. If A-=(5,7) , then find the equation of side B Cdot

The equation of a line which is parallel to the line common to the pair of lines given by 6x^2-x y-12 y^2=0 and 15 x^2+14 x y-8y^2=0 and at a distance of 7 units from it is (a) 3x-4y=-35 (b) 5x-2y=7 (c) 3x+4y=35 (d) 2x-3y=7

A possible equation of L is (A) x 3y 1 (B) x 3y 1 (C) x 3y 1 (D) x 3y 5