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Parabola Calculator ( Parabola Grapher Online )Parabola Vertex Focus Calculator Formulas (Y = aX2 + bX + c, a≠0) • Focus X = -b/2a Parabola equation and graph with major axis parallel to y axis. If a>0, parabola is upward, a<0, parabola is downward. If the major axis is parallel to the x axis, interchange x and y during your calculation. click here for parabola equation solver. Segment of a Parabola Calculator Segment of a Parabola Formulas • Area = 2 * h * b; Given the focus and directrix of a parabola , how do we find the equation of the parabola? If we consider only parabolas that open upwards or downwards, then the directrix will be a horizontal line of the form y = c . Let ( a , b ) be the focus and let y = c be the directrix. Let ( x 0 , y 0 ) be any point on the parabola.
Any point, ( x 0 , y 0 ) on the parabola satisfies the definition of parabola, so there are two distances to calculate:
To find the equation of the parabola, equate these two expressions and solve for y 0 . Find the equation of the parabola in the example above. Distance between the point ( x 0 , y 0 ) and ( a , b ) : ( x 0 − a ) 2 + ( y 0 − b ) 2 Distance between point ( x 0 , y 0 ) and the line y = c : | y 0 − c | (Here, the distance between the point and horizontal line is difference of their y -coordinates.) Equate the two expressions. ( x 0 − a ) 2 + ( y 0 − b ) 2 = | y 0 − c | Square both sides. ( x 0 − a ) 2 + ( y 0 − b ) 2 = ( y 0 − c ) 2 Expand the expression in y 0 on both sides and simplify. ( x 0 − a ) 2 + b 2 − c 2 = 2 ( b − c ) y 0 This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite with ( x , y ) . Therefore, the equation of the parabola with focus ( a , b ) and directrix y = c is ( x − a ) 2 + b 2 − c 2 = 2 ( b − c ) y Example: If the focus of a parabola is ( 2 , 5 ) and the directrix is y = 3 , find the equation of the parabola. Let ( x 0 , y 0 ) be any point on the parabola. Find the distance between ( x 0 , y 0 ) and the focus. Then find the distance between ( x 0 , y 0 ) and directrix. Equate these two distance equations and the simplified equation in x 0 and y 0 is equation of the parabola. The distance between ( x 0 , y 0 ) and ( 2 , 5 ) is ( x 0 − 2 ) 2 + ( y 0 − 5 ) 2 The distance between ( x 0 , y 0 ) and the directrix, y = 3 is | y 0 − 3 | . Equate the two distance expressions and square on both sides. ( x 0 − 2 ) 2 + ( y 0 − 5 ) 2 = | y 0 − 3 | ( x 0 − 2 ) 2 + ( y 0 − 5 ) 2 = ( y 0 − 3 ) 2 Simplify and bring all terms to one side: x 0 2 − 4 x 0 − 4 y 0 + 20 = 0 Write the equation with y 0 on one side: y 0 = x 0 2 4 − x 0 + 5 This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite with ( x , y ) . So, the equation of the parabola with focus ( 2 , 5 ) and directrix is y = 3 is y = x 2 4 − x + 5 Parabola is a locus of all points which are equally spaced from a fixed line and a fixed point. Parabola is obtained by slicing a cone parallel to the edge of the cone. What is a Parabola Calculator?'Parabola Calculator' is an online tool that helps to construct the graph of the given parabola equation. Online Parabola calculator assists you to graph the parabola in a few seconds. Parabola CalculatorHow to Use Parabola Calculator?Please follow the below steps to graph the parabola:
How to Plot a Parabola?Parabola is obtained by slicing a cone parallel to the edge of the cone. It is of U – shape as a stretched geometric plane. The formula of a parabola is : y = x2 (on the x-y axis) For parabola, eccentricity is 1, that is, a : b = 1 Here, a is the perpendicular distance from the focus to a point on the curve and b is the distance from the directrix to the point. Want to find complex math solutions within seconds? Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Book a Free Trial Class Solved Example on Parabola CalculatorExample: Plot the parabola given by the equation y2 − 4y + 4x − 4 = 0 Solution: The given equation can be rearranged as (y - 2)2 = -4(x - 2) This represents a parabola with vertex V(2, 2) and opening towards the left because a = –1 (negative). The focus will lie at a distance of 1 unit to the left of (2, 2), i.e., at (1, 2). The directrix will lie 1 unit to the right of (2, 2), i.e. it will be x = 3. The following figure shows this parabola: ☛ Related Articles:
☛ Math Calculators:How do you find the focus and directrix of a parabola?The standard form is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.
How do you find the focus of a parabola calculator?In order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x−h)2+k where a represents the slope of the equation. From the formula, we can see that the coordinates for the focus of the parabola is (h, k+1/4a).
How do you find the focus and Directrix and focal diameter of a parabola?use h,k , and p to find the coordinates of the focus, (h+p, k) use h and p to find the equation of the directrix, x=h−p. use h,k , and p to find the endpoints of the focal diameter, (h+p,k±2p)
What is the focus and Directrix of?What are the focus and directrix of a parabola? Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).
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