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The number of common tangent(s) to the circles `x^2+y^2+2x+8y-23=0`and `x^2+y^2-4x-10 y-19=0`is1 (b) 2(c) 3 (d)4A. `1`B. `2`C. `3`D. `4` |
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Answer» Correct Answer - C the number ber of ………… `x^(2)+y^(2)+2x+8y-23= 0` ………..(1) `x^(2)+y^(2)-4x-10y+19 = 0` ………..(2) `c_(1) -= (-1, -4)` , `r_(1) = sqrt(1+16+23) = 2sqrt(10)` `c_(2)-= (2, 5)` , `r_(2)= sqrt(4+25-19) = sqrt(10)` Here `c_(1)c_(2) = sqrt(9+81), r_(1)+r_(2)= 3sqrt(10)` Hence circles touch each other externally So there are 3 common tangent |
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