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If m is the slope of a common tangent to the curves x2/16 + y2/9 = 1 and x2 + y2 = 12, then 12m2 is equal to:(A) 6(B) 9 (C) 10 (D) 12 |
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Answer» Correct option is (B) 9 \(\frac{x^2}9+\frac{y^2}9=1\) equation of tangent to the ellipse is y = mx \(\pm\sqrt{a^2m^2+b^2}\) y = mx \(\pm\sqrt{16m^2+9}\)----(i) x2 + y2 = 12 equation of tangent to the circle is y = mx \(\pm\sqrt{12}\sqrt{1+m^2}\)--(ii) for common tangent equate eq. (i) and (ii) ⇒ 16m2 + 9 = 12(1 + m2) 16m2 - 12m2 = 3 4m2 = 3 12m2 = 9 |
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