Let `P` be the family of parabolas `y=x^2+p x+q ,(q!=0),` whose graphs cut the axes at three points. The family of circles through these three points have a common point (1, 0) (b) (0, 1) (c) (1, 1) (d) none of these

P, Q, and R are the feet of the normals drawn to a parabola ( y−3 ) ^2 =8( x−2 ) . A circle cuts the above parabola at points P, Q, R, and S . Then this circle always passes through the point. (a) ( 2, 3 ) (b) ( 3, 2 ) (c) ( 0, 3 ) (d) ( 2, 0 )

Property 4: The equation of the family of circles passing through two given points P(x_(1),y_(1)) and Q(x_(2),y_(2))

Let parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point (1,0) then b-c=

Suppose a parabola y = x^(2) - ax-1 intersects the coordinate axes at three points A,B and C, respectively. The circumcircle of DeltaABC intersects the y-axis again at the point D(0,t) . Then the value of t is

If 3a+2b+c=0 the family of straight lines ax+by+c=0 passes through the fixed point (p, q) then p + q

The family of straight lines 3(a+1)x-4(a-1)y+3(a+1)=0 for different valules of ' a ' passes through a fixed point whose coordinates are:- a.(1,0) b. (-1,0) c. (-1,-1) d. none of these

" The locus of the vertices of the family of parabolas " y=ax^(2)+2a^(2)x+1 " is " (a!=0) " a curve passing through the point "