Parabola - Study guides, Class notes & Summaries

Equation of a cricle (x-h)^2 + (y - k)^2 = r^2 Equation of a parabola (vertical) y - k = (1/4p)(x - h)^2 00:01 01:28 Equation of a parabola (horizontal) x - h = (1/4p)(y - k)^2 Focus A fixed point in the parabola DIrectrix A fixed line outside of the parabola Definition of a Circle The set of all points in a plane at a certain positive distance (radius) from a certain point (center) Definition of a Parabola The set of points equidistant ...

Circle Collection of points equidistant from the center. Equations for Circle (x-h)^2 + (y-k)^2 = r^2 Where (h,k) = center And r = radius 00:24 01:28 Distance Formula The square root of (x2-x1)^2 + (y2-y1)^2 Parabola Set of points equidistant from a focus and the directrix. Equations for Parabolas (x-h)^2 = 4p(y-k) Up if p>0, down if p<0 (y-k)^2 = 4p(x-h) Right if p>0, left if p<0 p = distance (h,k) = vertex Directrix E...

what is the equation for a circle in standard form? (x-h)^2 + (y-k)^2 = r^2 how do you find the center of a circle when the question is given to you in standard form? change the signs of the x and the y and put it in parentheses Ex: Q: (x+3)^2 + (y-1)^2 = 81 A: (-3, 1) 00:01 01:28 how do you find the radius of a circle when the question is given to you in standard form? take the number after the = and square root it how do you put an equation in standard for...

equation for parabola going through horizontal twice x²=4py equation for parabola going through vertical twice y²=4px 00:01 01:28 directrix of x²=4py y=-p directrix of y²=4px x=-p what is the symbol for focus? p the coordinates for the foci in x²=4py? (vertex,vertex±c) the coordinates for the foci in y²=4px? (vertex±c,vertex) what is p? the distance from the vertex to the focus what is the equation for a circle (x...

What is the equation for a circle? (x - h)^2 + (y - k)^2 = r^2 What is the midpoint formula? x1+x2/2 ; y1+y2/2 00:03 01:28 How do you know you are going to Graph a circle? If addition and if the coefficients are the same. How do you get the equation of a circle if it is not in standard form? Group the x and y's together then complete the square. How do you complete the square? Divide the middle coefficient by 2 and square it. Then add it to both sides ...

Axis of symmetry The line that a parabola is symmetrical about. The vertex and focus are on the axis of symmetry What is the equation of a circle with center at (3, -2) and radius = 8? (x - 3)² + (y + 2)² = 64 00:01 01:28 What is the equation of a circle with center at (-7, -1) and radius = 3? (x + 7)² + (y + 1)² = 9 What is the equation of a circle with center at (1, 5) and radius = 2? (x - 1)² + (y - 5)² = 4 What is the equation of a circle with ...

PRECALCULUS Study Questions with Answers Rational Number - Answer--any number that is a real number that can be written ass a terminating or repeating decimal Irrational Number - Answer--real number that cannot be written as a terminating or repeating decimal (square root of 5) Quadratic Formula - Answer--b±[√b²-4ac]/2a Factoring Cubes - Answer-a^3+b^3=(a+b) (a^2-ab+b^2) -if it is A^3-B^3 then change to (a-b)(a^2+ab+b^2) Discriminant - Answer--for quadratic expression, the d...

Circle A defined as a set of points that are equidistant (the same distance) from a certain point Hyperbola the set of points in a plane whose distances to two fixed points in the plane have a constant difference; a curve consisting of two distinct and similar branches, formed by the intersection of a plane with a right circular cone when the plane makes a greater angle with the base than does the generator of the cone. 00:01 01:28 Ellipse a plane curve such that the s...

(x-h)^2 + (y-k)^2= r^2 Circle graph formula syntax r What is the radius in a circle graph? 00:28 01:28 (h,k) What is the vertex in a circle graph? 1. Put all normal numbers on the right side 2. Make boxes for the x and y expressions 3. b/2 squared is put next to the expression and on the right 4. Put in x/y plus or minus b/2 and clean up right side How does one complete the square? When the x side is squared and p is positive When does the graph open...

1. A circle can be centered anywhere in the coordinate plane. ANSWER: True 2. Find the standard equation of the hyperbola which satisfies the given conditions: Vertices (-2, 8) and (8, 8), a focus (12, 8) ANSWER: (x−3)225−(y−8)256=1(x−3)225−(y−8)256=1 3.What are the coordinates of the center of the circle given by the equation x2+y2-16x- 8y+31=0? ANSWER: (8,4) 4.Give the standard equation of the circle satisfying the given condition: center at the origin, radius 4Give ...