Parabola `y^2=4a(x-c_1)` and `x^2=4a(y-c_2)` , where `c_1a n dc_2` are variable, are such that they touch each other. The locus of their point of contact is (a)`x y=2a^2` (b) `x y=4a^2` (c)`x y=a^2` (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact 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

Which one of the following curves cut the parabola at right angles? (a) x^2+y^2=a^2 (b) y=e^(-x//2a) (c) y=a x (d) x^2=4a y

If x=m x+c touches the parabola y^2=4a(x+a), then (a) c=a/m (b) c=a m+a/m (c) c=a+a/m (d) none of these

Two circle x^2+y^2=6 and x^2+y^2-6x+8=0 are given. Then the equation of the circle through their points of intersection and the point (1, 1) is (a) x^2+y^2-6x+4=0 (b) x^2+y^2-3x+1=0 (c) x^2+y^2-4y+2=0 (d)none of these

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is an (a)parabola (b) ellipse (c)hyperbola (d) circle

The parabolas y^2=4ac and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then (a) a+b+c=0 (b) a+b=2 (c) b-c=1 (d) a+c=-2

The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the point a) (4,3) b) (1/4,1/3) c) (1/2,1/3) d) none of these