If `a!=0` and the line `2b x+3c y+4d=0` passes through the points of intersection of the parabolas `y^2=4a x` and `x^2=4a y ,` then (a)`d^2+(2b+3c)^2=0` (b)`d^2+(3b+2c)^2=0` (c)`d^2+(2b-3c)^2=0` (d)none of these

The locus of the midpoint of the segment joining the focus to a moving point on the parabola y^2=4a x is another parabola with directrix (a) y=0 (b) x=-a (c) x=0 (d) none of these

The equation of the circle passing through the point of intersection of the circles x^2+y^2-4x-2y=8 and x^2+y^2-2x-4y=8 and the point (-1,4) is (a) x^2+y^2+4x+4y-8=0 (b) x^2+y^2-3x+4y+8=0 (c) x^2+y^2+x+y=0 (d) x^2+y^2-3x-3y-8=0

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

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

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

Which of the following line can be tangent to the parabola y^2=8x ? (a) x-y+2=0 (b) 9x-3y+2=0 (c) x+2y+8=0 (d) x+3y+12=0

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then (a) 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

The locus of the image of the point (2,3) in the line (x-2y+3)+lambda(2x-3y+4)=0 is (lambda in R) (a) x^2+y^2-3x-4y-4=0 (b) 2x^2+3y^2+2x+4y-7=0 (c) x^2+y^2-2x-4y+4=0 (d) none of these

If the planes x-c y-b z=0,c x-y+a z=0a n d b x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b c dot