Equation of the common tangent to the ellipse x216+y29=1 and the circle x2+y2=12 is
A
2y=√3x+√21
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B
√3y=2x+√21
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C
√3y=2x−√21
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D
y
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Solution
The correct option is A2y=√3x+√21 Equation of tangent to the ellipse x216+y29=1 is y=mx±√16m2+9 ⇒mx−y±√16m2+9=0 If it is also Tangent to the circle x2+y2=12 then r = d holds good, ∴√12=√16M2+9√M2+1 ⇒12(m2+1)=16m2+9 ⇒m2=34⇒m=±√32 ∴Tangentis2.y=√3x±√21