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 `x=5` (b) `x-y=5` `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 .

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 .

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

A B C is a variable triangle such that A is (1, 2), and Ba n dC on the line y=x+lambda(lambda is a variable). Then the locus of the orthocentre of "triangle"A B C is x+y=0 (b) x-y=0 x^2+y^2=4 (d) x+y=3

In triangle A B C , the equation of side B C is x-y=0. The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is a) x^2+y^2-4x+6y-27=0 b) x^2+y^2-4x-6y-27=0 c) x^2+y^2+4x-6y-27=0 d) x^2+y^2+4x+6y-27=0

ABC is a variable triangle such that A is (1, 2), and B and C on the line y=x+lambda(lambda is a variable). Then the locus of the orthocentre of DeltaA B C is (a) x+y=0 (b) x-y=0 x^2+y^2=4 (d) x+y=3

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

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 (a) y=x (b) 5x+y+12=0 (c) x+5y-4=0 (d) x+5y+12=0

The equations of the sides A B ,\ B C\ a n d\ C A\ of\ "triangle"A B C\ a r e\ y-x=2,\ x+2y=1\ a n d\ 3x+y+5=0 respectively. The equation of the altitude through B is x-3y+1=0 b. x-3y+4=0 c. 3x-y+2=0 d. none of these

Prove that the line 5x-2y-1=0 is mid-parallel ot the lines 5x-2y-9=0a n d 5x-2y+7=0.