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Equation of parabola with vertex and y-intercept. Equation of parabola with vertex and point. Equation of parabola with vertex and focus. Equation of parabola with vertex not at origin. Equation of parabola with vertex and focus calculator. The equation of a parabola can be expressed in either standard or vertex form as shown in the picture Axis: Negative y-axis. Thus, we can derive the equations of the parabolas as: y 2 = 4ax. y 2 = -4ax. x 2 = 4ay. x 2 = -4ay. These four equations are called standard equations of parabolas. It is important to note that the standard equations of parabolas focus on one of the coordinate axes, the vertex at the origin. The graph with equation y — kx2 is shown below. —16) The point (2, —16) lies on the graph. Determine the value of k. A parabola has equation y = x —8x+19. (a) Write the equation in the form y = (x— (b) Sketch the graph of y=x2 —8x+19, p)2+q. showing the coordinates of the 5 turning point and the point of intersection with the y-axis. coursehero.com Browse Example 2 If the equation of the parabola is x2 = - 8y, find coordinates of the focus, the equation of the directrix and length of latus rectum. Solution The given equation is of the form x2 = - 4ay where a is positive. Therefore, the focus is on y-axis in the negative direction and parabola opens downwards. 194 EXEMPLAR PROBLEMS - MATHEMATICS Comparing the given equation with standard • Given an equation of a hyperbola in a form like (x+4)2 16 (y1)2 4 = 1, find its vertices and center. • Given an equation in a form like 4x2 9y2 + 8x 36y = 6, complete the square to put it in the form (xh)2 a2 (yk) b2 = 1 • Given an equation in the form the form (xh)2 a2 (yk) b2 = 1, draw its graph. • Write down the equation for a Write the equation of the parabola with focus (-3, 1), and vertex (-4, 1). 4. Write the equation of a parabola with focus at (-2, 0) and line of directrix is x = 4Focus 5. The cross section of a television antenna dish is a parabola. For one dish, the receiver is located at the focus, 4 feet above the vertex.