# show that the line X + Y equal to 8 intersect the parabola y square equal to 4 x at two points P and Q find the coordinates of the point equation of the chord PQ and its length is

Aarya
30 Points
5 years ago
X+Y=8
X=8-Y--------------(1)
Y^2=4X
Y^2=4(8-Y)
Y^2+4Y-32=0
ON FINDING ROOTS, WE GET, Y=-8,+4
SUBSTITUTING IN (1),
IF Y=-8, X=16
IF Y=+4, X=4
HENCE, P=(16,-8)
Q=(4,4)
PQ=√[(16-4)^2+(-8-4)^2]
PQ=√(144+144)
PQ=12√2 SQ.UNITS
The text passage contains a mathematical question about the intersection of a line and a parabola, and it provides a detailed solution including the coordinates of the points of intersection and the length of the chord PQ.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# show that the line X + Y equal to 8 intersect the parabola y square equal to 4 x at two points P and Q find the coordinates of the point equation of the chord PQ and its length is

Aarya
30 Points
5 years ago
X+Y=8
X=8-Y--------------(1)
Y^2=4X
Y^2=4(8-Y)
Y^2+4Y-32=0
ON FINDING ROOTS, WE GET, Y=-8,+4
SUBSTITUTING IN (1),
IF Y=-8, X=16
IF Y=+4, X=4
HENCE, P=(16,-8)
Q=(4,4)
PQ=√[(16-4)^2+(-8-4)^2]
PQ=√(144+144)
PQ=12√2 SQ.UNITS
user
The text passage contains a mathematical question about the intersection of a line and a parabola, and it provides a detailed solution including the coordinates of the points of intersection and the length of the chord PQ.

TYPE: SINGLE_QUESTION_WITH_ANSWER