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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

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

Grade:11

1 Answers

Aarya
30 Points
4 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

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