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Question

The number of tangents to the circle x2+y2=3 that are normals to the ellipse x29+y24 is

A
one
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B
two
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C
three
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D
zero
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Solution

The correct option is A one
Let y = mx+c is tangent to x2+y2=3
Then by condition of tangeney
cm2+1=3
c2=3(m2+1) __(1)
y=mx+c is Normal to x29+y24=1
If
c=(b2a2)ma2+b2m2
c=(49)m9+4m2
c2=25m24m2+9
3(m2+1)(4m2+9)=25m2
let m2=t
3(t+1)(4t+9)=25t
since, D<0.
Hence, There is no root :
Hence, There is no tangent to circle which is
Normal to ellipse.

1089943_1189729_ans_e35791544f514627baf32928651e1e0c.png

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