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Tangent to the parabola `y=x^(2)+ax+1` at the point of intersection of the y-axis also touches the circle `x^(2)+y^(2)=r^(2)`. Also, no point of the parabola is below the x-axis. The slope of the tangents when the radius of the circle is maximum isA. -1B. 1C. 0D. 2 |
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Answer» Correct Answer - C (3) The equation of the tangent at (0,1) to the parabola `y=x^(2)+ax+1` is y-1=a(x-0) `orax-y+1=0` As it touches the circle, we get `r=(1)/(sqrt(a^(2)+1))` The radius is maximum when a=0. Therefore, the equation of the tangent is y=1. Therefore, the slope of the tangent is 0. |
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