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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 radius of circle when a attains its maximum value isA. `1//sqrt(10)`B. `1//sqrt(5)`C. 1D. `sqrt(5)` |
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Answer» Correct Answer - B (2) Since no point of the parabola is below the x-axis, `D=a^(2)-4le0` Therefore, the maximum value of a is 2. The equation of the parabola when a=2 is `y=x^(2)+2x+1` It intersect the y-axis at (0,1). The equation of the tangent at (0,1). y=2x+1 Since y=2x+1 touches the circle `x^(2)+y^(2)=r^(2)`, we get `r=(1)/(sqrt(5))` |
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