If the line y=mx+a meets the parabola y2=4ax at two points whose abscissas are x1 and x2, then x1+x2=0 if
A
m=−1
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B
m=1
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C
m=2
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D
m=−12
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Solution
The correct option is Cm=2 Given line is y=mx+a⋯(1) y2=4ax⋯(2)
Substitute y from equation (1) into equation (2) (mx+a)2=4ax ⇒m2x2+2amx+a2=4ax ⇒m2x2+(2am−4a)x+a2=0
For x1+x2=0,
Sum of roots =0 ⇒−2am−4am2=0 ⇒4a−2am=0 ⇒m=2