A parabola is the set of all points that ?
2 answers:
Answer:
A parabola is the set of all points in the plane equidistant from a given line and a given point not on the line.
A parabola is the set of all points in the plane equidistant from directrix and focus.
Step-by-step explanation:
A parabola is the set of all points in the plane equidistant from a given line and a given point not on the line.
The line is called directrix and the point is called focus.
So a parabola is the set of all points in the plane equidistant from directrix and focus.
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To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.
<h3>Distribute</h3>Use the distributive property to distribute 3x into the term (x + 6):
To create a quadratic equation, add 10 to both sides of the equation:
The quadratic formula is defined as:
The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.
Therefore:
- a = 3
- b = 18
- c = 10
Set up the quadratic formula:
Simplify by using BPEMDAS, which is an acronym for the order of operations:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Use BPEMDAS:
Simplify the radicand:
Create a factor tree for 204:
204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.
The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:
Then, using the Product Property of Square Roots, break this into two radicands:
Since 4 is a perfect square, it can be evaluated:
To simplify further for easier reading, remove the multiplication symbol:
Then, substitute for the quadratic formula:
This gives us a combined root, which we should separate to make things easier on ourselves.
<h3>Separate the Roots</h3>Separate the roots at the plus-minus symbol:
Then, simplify the numerator of the roots by factoring 2 out:
Then, simplify the fraction by reducing 2/6 to 1/3:
The final answer to this problem is: