Section 5 - Topic 7Writing Quadratic Equations when Given a Focus andDirectrix1. Marsha was completing the steps for a parabola that has a focus at(5, –2) with directrix at y = -3. Complete the missing steps below.The distance from focus to a point on the line (x, y):d = C- x)² + L-y)²The distance from the point on the line (x,y) to the directrix:d =,)² + (y – (-3))²The distance from focus to point on line is equal to the distance from directrixto point on line.C- x)² + _ - y)² = d = J-D? + (y – (-3)²L-x)? + (_- y)? = (__- -)² + (y – (-3))²- 10x + x² + 4 + + y? = (__)² + + 6y + 9x² + y? + 4y + = y? +,x² – 10x + 29 =x² – 10x + = 2y_(x² – 10x + 20) = yFunction of the parabola:f(x) = ._x².x+.

Formula:-1)Distance between two points (x1,y1) & x2,y2 is d=(x1-x2)2+(y1-y2)22)Distance of a…

Answered: 1. Marsha was completing the steps for…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Concept explainers

Question

Section 5 - Topic 7
Writing Quadratic Equations when Given a Focus and
Directrix
1. Marsha was completing the steps for a parabola that has a focus at
(5, –2) with directrix at y = -3. Complete the missing steps below.
The distance from focus to a point on the line (x, y):
d = C- x)² + L-y)²
The distance from the point on the line (x,y) to the directrix:
d =,
)² + (y – (-3))²
The distance from focus to point on line is equal to the distance from directrix
to point on line.
C- x)² + _ - y)² = d = J
-D? + (y – (-3)²
L-x)? + (_- y)? = (__- -
)² + (y – (-3))²
- 10x + x² + 4 + + y? = (__)² + + 6y + 9
x² + y? + 4y + = y? +,
x² – 10x + 29 =
x² – 10x + = 2y
_(x² – 10x + 20) = y
Function of the parabola:
f(x) = .
_x².
x+.

Expert Solution

Step 1

$F o r m u l a : - 1) D i s \tan c e b e t w e e n t w o p o i n t s (x_{1}, y_{1}) & (x_{2}, y_{2}) i s d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} 2) D i s \tan c e o f a p o i n t (α, β) f r o m a l i n e a x + b y + c = 0 i s d = \pm \frac{α a + β b + c}{\sqrt{a^{2} + b^{2}}} T h e r e f o r e d i s \tan c e o f a p o i n t (α, β) f r o m t h e l i n e y = c i s d = \pm \frac{β - c}{\sqrt{0^{2} + 12}} = \pm (β - c) = |(β - c)| = \sqrt{{(β - c)}^{2}} = \sqrt{0^{2} + {(β - c)}^{2}} d = \sqrt{{(0 - 0)}^{2} + {(β - c)}^{2}}$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Parabolas$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions