Shifted and general parabola

JEE Main Mathematics · Parabola · 6 questions, latest first

• Let the image of parabola x^2=4 y, in the line x-y=1 be (y+a)^2=b(x-c), a, b, c ∈ N. Then a+b+c is equal to202624 January, Shift 2 · Q11
• Let P be the parabola, whose focus is (-2,1) and directrix is 2 x+y+2=0. Then the sum of the ordinates of the points on P, whose…20257 April, Shift 1 · Q10
• The axis of a parabola is the line y=x and its vertex and focus are in the first quadrant at distances √2 and 2 √2 units from the…20254 April, Shift 2 · Q9
• Two parabolas have the same focus (4,3) and their directrices are the x -axis and the y -axis, respectively. If these parabolas…202529 January, Shift 1 · Q12
• Let A and B be the two points of intersection of the line y+5=0 and the mirror image of the parabola y^2=4 x with respect to the…202528 January, Shift 2 · Q23
• If the equation of the parabola with vertex V(3/2, 3) and the directrix x+2 y=0 is α x^2+β y^2-γ x y-30 x-60 y+225=0, then α+β+γ…202524 January, Shift 2 · Q12