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If the circle `x^2 + y^2 + ( 3 + sin beta) x + 2 cos alpha y = 0` and `x^2 + y^2 + 2 cos alpha x + 2 c y = 0` touch each other, then the maximum value of c is |
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Answer» Correct Answer - 1 `x^(2)+y^(2)+(3+sin beta )x +(2 cos alpha) y =0` (1) `x^(2)+y^(2)+(2 cos alpha ) x +2cy =0` (2) Since both the circles are passing through the origin (0,0) , the equation of tangent to circles at (0,0) will be same . Tanget at (0,0) to circle (1) is, `(3 sin beta )x + (2 cos alpha ) y =0` (3) Tangent at (0,0) to circle (2) is `(2 cos alpha )x +2cy =0` Therefore, (1)/ and (2), we get `(3+sin beta)/(2 cos alpha )=(2c os alpha)/(2c)` or `c=(2cos^(2)alpha)/(3+sin beta)` `:. c_("max")=1` when `sin beta = -1 ` and `alpha =0` |
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