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SOLVED:In Exercises 5 through 14, the equation is that of a conic having a focus at the pole. In each Exercise, (a) find the eccentricity; (b) identify the conic; (c) write an equation of the directrix which corresponds to the focus at the pole; (d) draw a sketch of the curve. r=(5)/(2 sinθ)
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(a) Show that any conic in 𝐀^2 is isomorphic either to 𝐀^1 or 𝐀^1-; 0, (cf. Ex. 1.1 ). (b) Show that 𝐀^1 is n o t isomorphic to any proper open subset of itself. (This result is generalized by (Ex. 6.7 ) below.) (c) Any conic in 𝐏^2 is isomorphic to 𝐏^1 (d) We will see later (Ex. 4.8 ) that any two curves are homeomorphic. But show now that 𝐀^2 is not even homeomorphic to 𝐏^2 (e) If an affine variety is isomorphic to a projective variety, then it consists of only one point. | Numerade
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