Find the equation of parabola (i) having end points of latus rectum (5,10) and (5,-10) and which opens towards right. (ii) having vertex at origin and focus at (0,2)
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(i) Here, focus S(0,-3) and directrix y=3 are at same distance from origin is vertex of the parabola and parabola opens downwards. So, we consider equation `x^(2)=-4ay`. Here focus is `(0,-3)-=(0,-a)` `:." "a=3` So, equation of parabola is `y^(2)=-12x`. (ii) End points of latus are A (5,10) and B (5,-10). `:." "S-=(5,0)` Also, parabola opens towards right. So, we consider equation `y^(2)=4ax`. `:.` Vertex is (0,0) and a=5. So, equation of parabola is `y^(2)=20x`. (iii) Vertex is (0,0) focus S(0,2). So, directrix is y=-2. So, we consider equation `x^(2)=4ay`, where a=2. `:.` Equation of parabola is `x^(2)=8y`.
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