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**parabola**is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight**line**which is known as the directrix.**Parabola**is an integral part of conic section topic and all its concepts**parabola**are covered here. TABLE OF CONTENTS. Definition; Standard Equation; Latus Rectum **Parabola****A****parabola**is defined as a collection of points such that the distance to a fixed point (the focus) and a fixed straight**line**(the directrix) are equal. But it's probably easier to remember it as the U-shaped curved**line**created when a quadratic is graphed. Many real-world objects travel in a parabolic shape.**A Line and a Parabola**.Let the equation of a**parabola**be \[y^2=4ax\] and, the equation of**a line**be \[y=mx+c\] Now, let us solve these two equations simultaneously to obtain the points of intersection of the**parabola**and the**line**.. .**Parabola**Opens Right. Standard equation of a**parabola**that opens right and symmetric about x-axis with vertex at origin. y 2 = 4ax.- The equation of the
**parabola**with focus at and vertex at is. The latus rectum points are points on the**parabola**that are in**line**with the focus. By my drawing, you notice that the two points that define the latus rectum and the focus share the same x-coordinate. This is only true when the**parabola**is oriented horizontally as in this example. - No Intersection Between a
**Line**and**Parabola**. The**line**y = m x + c does not intersect the**parabola**y 2 = 4 a x if a < m c. Consider that the standard equation of a**parabola**with vertex at origin ( 0, 0) can be written as. y 2 = 4 a x โ โ โ ( i) Also the equation of a