Answer: The equation of a parabola with vertex at the origin and symmetric about the y-axis is x2 = 4ay The point P(5,2) passes through above parabola, 52 =...
Find the equation of the parabola with vertex at the origin and focus F(0, 5).
Answer: Vertex : A (0,0) Focus F(0,5) is of the form F(0,a) Vertex A(0,0) and Focus F(0,a), The equation of parabola is x2 = 4ay a = 5 The equation of parabola is...
Find the equation of the parabola with focus F(0, -3) and directrix y = 3.
Answer: Given, The equation of directrix is, y = 3 y - 3 = 0 Above equation is of the form, y - a = 0 Focus of the parabola F(0,-3) is of the form F(0,-a) a = 3...
Find the equation of the parabola with focus F(4, 0) and directrix x = -4.
Answer: Given, Equation of directrix, x = -4 x + 4 = 0 The equation is of the form, x + a = 0 Focus of the parabola F(4,0) is of the form F(a,0) a = 4 For...
Find the equation of the parabola with vertex at the origin and focus at F(-2, 0).
Answer : Vertex : A (0,0) focus F(-2,0) is of the form F(-a,0) For Vertex A(0,0) and Focus F(-a,0), The equation of parabola is y2 = - 4ax a = 2 The equation of...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, 3x2 = -16y x2 = -16/3 y Comparing the given equation with parabola having an equation, x2 = 4ay 4a = 16/2 a = 4/3 Focus: F(0, -a) = F(0, -4/3) Vertex: A(0,...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, x2 = -18y Comparing given equation with parabola having equation, x2 = -4ay 4a = 18 a = 9/2 Focus: F(0, -a) =F(0, -9/2) Vertex: A(0, 0) =A(0, 0) Equation...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, x2 = - 8y Comparing given equation with parabola having equation, x2 = - 4ay 4a = 8 a = 2 Focus : F(0,-a) = F(0,-2) Vertex : A(0,0) = A(0,0) Equation of...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, 3x2 = 8y x2 = 8/3 y Comparing the given equation with parabola having an equation, x2 = 4ay 4a = 8/3 a = 2/3 Focus : F(0, a) = F(0, 2/3) Vertex :...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, x2 = 10y Comparing given equation with parabola having equation, x2 = 4ay 4a = 10 a = 5 Focus : F(0,a) = F(0,2.5) Vertex : A(0,0) = A(0,0) Equation of the...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, x2 = 16y Comparing given equation with parabola having equation, x2 = 4ay 4a = 16 a = 4 Focus : F(0,a) = F(0,4) Vertex : A(0,0) = A(0,0) Equation of the...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, 5y2 = -16x y2 = -16/5 x Comparing the given equation with parabola having an equation, y2 = - 4ax 4???? = 16/5 ???? = 4/5 Focus : F(-a,0) = F(-4/5, 0)...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, y2 = -6x Comparing given equation with parabola having equation, y2 = - 4ax 4a = 6 a = 2/3 Focus: F(-a, 0) = F(-2/3, 0) Vertex: A(0, 0) =A(0, 0)...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
Answer: Given, y2 = -8x Comparing given equation with parabola having equation, y2 = - 4ax 4a = 8 a = 2 Focus : F(-a,0) = F(-2,0) Vertex : A(0,0) = A(0,0) Equation...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola:
Answer: Given, 3y2 = 8x y2 = 8/3 x Comparing the given equation with parabola having equation, y2 = 4ax 4a = 8/3 a = 2/3 Focus : F(a, 0) = F(2/3, 0) Vertex :...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola:
Answer: Given, y2 = 10x Comparing given equation with parabola having equation, y2 = 4ax 4a = 10 a =2.5 Focus : F(a,0) = F(2.5,0) Vertex : A(0,0) = A(0,0) Equation of the...
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola:
Answer: Given, y2= 12x Comparing given equation with parabola having equation, y2 = 4ax 4a = 12 a = 3 Focus : F(a,0) = F(3,0) Vertex : A(0,0) = A(0,0) Equation of...
Find the equation of the parabola, which is symmetric about the y-axis and passes through the point P(2, -3).
Answer: The equation of a parabola with vertex at the origin and symmetric about the y-axis is x2 = 4ay The point P(2,-3) passes through above parabola, 22...