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Question

If the line y=x is a tangent to the parabola y=ax2+bx+c at the point (1,1) and the curve passes through (1,0), then

A
a=b=1, c=3
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B
a=b=12, c=0
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C
a=c=14, b=12
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D
a=0, b=c=12
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Solution

The correct option is C a=c=14, b=12
y=x is a tangent
slopes are equal.
dydx=2ax+b
1=2a+b at (1,1)(1)
Also, the parabola passes through (1,1)
a+b+c=1(2)
The parabola passes through (1,0)
0=ab+c(3)
Solving (1),(2),(3), we get -
a=c=14
and b=12

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