SOLUTION: Find all points on the y-axis that are a distance 7 from P(5, 9).
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Question 992588
:
Find all points on the y-axis that are a distance 7 from P(5, 9).
Answer by
macston(5194)
(
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):
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.
Point(
,
)=(
,
)
Point(
.
)=(
,
)
d=distance=7
.
.
Solved by
pluggable
solver:
SOLVE quadratic equation with variable
Quadratic equation
(in our case
) has the following solutons:
For these solutions to exist, the
discriminant
should not be a negative number.
First, we need to compute the discriminant
:
.
Discriminant d=96 is greater than zero. That means that there are two solutions:
.
Quadratic expression
can be factored:
Again, the answer is: 13.8989794855664, 4.10102051443364. Here's your graph:
.
y=4.1 or 13.9
.
ANSWER: There are two points: (0,4.1) and (0,13.9)
.