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Question

If the largest to the parabola y2=x at a point (α,β),(β>0) is also a tangent to the ellipse, x2+2y2=1, then α to:

A
22+1
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B
21
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C
2+1
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D
221
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Solution

The correct option is C 2+1
T:y(β)=12(x+β2)
2yβ=x+β2
y=(12β)x+β2
m=12β,C=β2
β2=±14β2+12β24=14β2+12β24=1+2β24β2
β42β21=0(β21)2=2β2=2+1
1250226_1614447_ans_be0ac3203e9c44b5b936437bc3db59d2.png

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