题目

求过定圆内一定点，且与定圆相切的圆心的轨迹的极坐标方程. 答案：思路分析：需要找圆心P的极角和极径的关系.在这里可以根据三角形中的余弦定理来建立关系式.解：以定圆圆心O为极点，定点为点A.求圆心P的轨迹.以射线OA为极轴建立极坐标系.设定圆半径为r，A(m,0),P(ρ,0)，在△AOP中，|AP|2=|OA|2+|OP|2-2|OA|·|OP|cosθ，即(r-ρ)2=m2+ρ2-2mρcosθ.化简得ρ=.当m取不同数值时，轨迹会In Wiltshire, England, volunteers are being sought to visit a nature protection area to count the butterflies living there and on surrounding fields. The project is promoted by an environmental protection organisation，which has contributed to improving the living environment for wild animals. Recently, the organisation has issued an appeal to help it observe environmental changes based on the record of butterflies and protect the environment. In the area, the local people have planted many special flowers with the help of the organisation, aiming to see whether these flowers will interest the rare and beautiful butterflies. The Project officer Sarah Marshall says, “It will be a suitable habitat for butterflies. They are great ‘indicator species’ as they are easily affected by climate changes so they make a brillian early - warning system for the environment.” She also points out that volunteers are needed to recourd the number or species of butterflies，and based on the change happening to the butterflies, the hidden environmental problems in the area can be found out in time. The organisation is seeking volunteers to help monitor butterflies from April through to September. They will walk a fixed route and record the different butterflies they encounter along the way.Each visit should take no more than two hours, and each volunteer is expected to visit once a month to count the wildlife. “Staff will provide back up, so if the weather is poor on the day you are to visit（butterflies don’t like to fly in the rain, wind or if it’s too cloudy) we can have someone else do your job,” Sarah points out. No previous experience is necessary as training and support will be provided，but a keen interest is essential. If you are interested, P1ease contact Sarah on (0l380) 725670，ext 278, email sarahm wiltshirewildlife. org 1.According to Paragraph l， what is the purpose of the Project? A．To appeal to more visitors. B．To protect the environment. C．To control butterfly population. D．To expand the area for wildlife. 2.Many special flowers have been planted in Wiltshire to           . A．warn people of wildlife extinction B．appeal more tourists to be involved in C．attract many unusual and beautiful butterflies D．improve the economic conditions of local people 3.Butterflies are called “indicator species” because              . A．they can provide support for visitors B．they can give information to other species C．they are not easily found out in their habitats D．they are very sensitive to environmental changes 4.What is the text mainly about? A．Visitors are being trained to identify butterflies. B．Wildlife areas are being protected by butterflies. C．Volunteers are being needed to count butterflies. D．Organisations are being put up to protect butterflies.