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The range of g so that we have always a chord of contact of tangents drawn from a real point `(alpha, alpha)` to the circle `x^(2)+y^(2)+2gx+4y+2=0`, isA. (-3, 0)B. (-4, 1)C. (-4, 0)D. none of these |
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Answer» Correct Answer - C For a real chord of contact of tangents drawn from `(alpha, alpha)` to the circle `x^(2)+y^(2)=2gx+4y+2=0`, the point `(alpha, alpha)` must lie outside the circle. `:. alpha^(2)+alpha^(2)+2g alpha + 4 alpha + 2 gt 0` `rArr alpha^(2)+g alpha + (2 alpha + 1) gt 0` `rArr alpha^(2)+(g+2)alpha+1gt0` Since `alpha` assumes real values . Therefore, `(g+2)^(2)-4 gt = 0` `rArr g^(2)+4h lt 0 rArr -4 lt g lt 0 rArr g in (-4, 0)`. |
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