双曲线x2a2-y2b2=1(a＞0，b＞0)的左右焦点为F1，F2，P是双曲线

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问题选择题

双曲线

=1(a＞0，b＞0)的左右焦点为F₁，F₂，P是双曲线上一点，满足|PF₂|=|F₁F₂|，直线PF₁与圆x²+y²=a²相切，则双曲线的离心率为（　　）

A．

B．

C．

D．

答案

设PF₁与圆相切于点M，因为|PF₂|=|F₁F₂|，所以△PF₁F₂为等腰三角形，
所以|F₁M|=

|PF₁|，
又因为在直角△F₁MO中，|F₁M|²=|F₁O|²-a²=c²-a²，所以|F₁M|=b=

|PF₁|①
又|PF₁|=|PF₂|+2a=2c+2a ②，

c²=a²+b² ③
由①②③解得

．

故选D．

单项选择题

Monroe, despite his generally poor appetite, thoroughly enjoyed the three meals he ate at the Tip-Top Restaurant, but, unfortunately, after each meal he became ill. The first time he ate an extra-large sausage pizza with a side order of hot peppers; the second time he took full advantage of the all-you-can-eat fried shrimp and hot peppers special; and the third time he had two of Tip-Top’s gaint meatball sandwiches with hot peppers. Since the only food all three meals had in common was the hot peppers, Monroe concludes that it is solely due to Tip-Top’s hot poppers that he became ill.
Monroe’s reasoning is most vulnerable to which one of the following criticisms

A．He draws his conclusion on the basis of too few meals that were consumed at Tip-Top and that included hot peppers.

B．He posits a causal relationship without ascertaining that the presumed cause preceded the presumed effect.

C．He allows his desire to continue dining at Tip-Top to bias his conclusion.

D．He fails to establish that everyone who ate Tip-Top’s hot peppers became ill.

E．(E) He overlooks the fact that at all three meals he consumed what was, for him, an unusually large quantity of food.

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