If the parabola `y=ax^2+bx+c` has vertex at(4,2)and ` a in [1,3]` then the difference beteween the extreme value of abc is equal to

Focus of parabola y=ax^(2)+bx+c is

If the parabola y^(2) = 4ax passes through the point (4, 1), then the distance of its focus the vertex of the parabola is

If the area of the triangle inscribed in the parabola y^(2)=4ax with one vertex at the vertex of the parabola and other two vertices at the extremities of a focal chord is 5a^(2)//2 , then the length of the focal chord is

If A_(1) is the area of the parabola y^(2)=4ax lying between vertex and the latusrectum and A_(2) is the area between the latusrectum and the double ordinate x=2a, then (A_(1))/(A_(2)) is equal to

A chord of parabola y^(2)=4ax subtends a right angle at the vertex The tangents at the extremities of chord intersect on

Suppose a,b,c are such that the curve y=ax^(2)+bx+c is tangent to y=3x-3 at (1,0) and is also tangent to y=x+1 at (3,4). Then the value of (2a-b-4c) equals

ax^(2)+bx+c and cx^(2)+bx+a have common zeroes (roots) (a!=c) then the value of a^(3)+b^(3)+c^(3) is not equal to

AB is a chord of the parabola y^(2)=4ax with its vertex at A.BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is