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 paralle to the line y=mx and vertices P,Q and S are on the straight lines y=a, x=b and x=-b respectively. Find the locus of the vertex R.

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 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

The tangent to the curve y=x^2-5x+5. parallel to the line 2y=4x+1, also passes through the point :

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

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

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

In a triangle A B C , if A is (2,-1),a n d7x-10 y+1=0 and 3x-2y+5=0 are the equations of an altitude and an angle bisector, respectively, drawn from B , then the equation of B C is (a) a+y+1=0 (b) 5x+y+17=0 (c) 4x+9y+30=0 (d) x-5y-7=0

The line y=(3x)/4 meets the lines x-y+1=0 and 2x-y=5 at A and B respectively. Find Coordinates of P on y=(3x)/4 such that PA*PB=25.