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A common tangent to `9x^2-16y^2 = 144` and `x^2 + y^2 = 9`, isA. `y=(3)/(sqrt(3))X+(15)/(sqrt(7))`B. `y= 3 sqrt((2)/(7))x+(15)/(sqrt(7))`C. `y= 2 sqrt((3)/(7))x+15sqrt(7)`D. None of these |
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Answer» Correct Answer - B Hyperbola `(x^(2))/(16)-(y^(2))/(9)=1` any tangent to the hy perboile is ` y= mx +-sqrt(a^(2)m^(2)-b^(2))` `implies y= mx +-sqrt(16 m^(2)-9) ....(1)` it toches the circle `implies|(sqrt(16m^(2)-9))/(sqrt(m^(2)+1))|=3` `impliesm=3sqrt((2)/(7))` `therefore` Equation of common tangent is `y=3sqrt((2)/(7))x+(15)/(sqrt(7))` |
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