Maths-
General
Easy
Question
Length of the chord intercepted by the parabola y = x2 + 3x on the line x + y = 5 is
- 6
-
- 6
- None of these
Hint:
find the points of intersection of the chord with the parabola
The correct answer is: 6
6√2
Point of intersection :
y = x2 + 3x and x + y = 5
x= 5-y
y= (5-y)2+3(5-y)
x2+5x-x-5 = 0
x(x+5)-1(x+5)
x=1,-5
y=4,10
(1,4) and (-5,10)
Length of chord = distance between the points of intersection.
= √(10-4)2+(-5-1)2 = 6√2
the distance between any two points is given by
√(x2-x1)2+(y2-y1)2
this formula is applied to the points of intersection which were calculated by solving the two equations .
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