心形线的极坐标方程是什么？
心形线的平面直角坐标系方程表达式分别为
x^2+y^2+a*x=a*sqrt(x^2+y^2)
和
x^2+y^2-a*x=a*sqrt(x^2+y^2）
极坐标方程
水平方向：
ρ=a(1-cosθ) 或 ρ=a(1+cosθ) (a>0)
垂直方向：
ρ=a(1-sinθ) 或 ρ=a(1+sinθ) (a>0)
绛旓細蟻=a(1+cos胃)杩欐槸蹇冨舰绾跨殑鏋佸潗鏍囨柟绋锛岃〃绀轰綘鏄垜鐨勬墍鐖便傝В绛旇繃绋嬪涓嬶細蹇冨舰绾匡紝鏄竴涓渾涓婄殑鍥哄畾涓鐐瑰湪瀹冪粫鐫涓庡叾鐩稿垏涓斿崐寰勭浉鍚岀殑鍙﹀涓涓渾鍛ㄦ粴鍔ㄦ椂鎵褰㈡垚鐨勮建杩癸紝鍥犲叾褰㈢姸鍍忓績褰㈣屽緱鍚嶃傛瀬鍧愭爣鏂圭▼锛氾紙1锛夋按骞虫柟鍚戯細 蟻=a(1-cos胃) 鎴 蟻=a(1+cos胃) (a>0)銆傦紙2锛夊瀭鐩存柟鍚戯細 蟻...
绛旓細蹇冨舰绾跨殑鏋佸潗鏍囨柟绋:蟻=a(1鍗乧os胃)涓よ竟鍚屾椂涔樹互蟻:蟻²=a(蟻鍗佅乧os胃)鍖栨垚鐩磋鍧愭爣鏂圭▼:x²鍗亂²=a[鈭(a²鍗亂²)鍗亁]
绛旓細濡備笅锛1銆佺洿瑙掑潗鏍囨柟绋 蹇冨舰绾跨殑骞抽潰鐩磋鍧愭爣绯绘柟绋嬭〃杈惧紡鍒嗗埆涓 锛歺^2+y^2+a*x=a*sqrt(x^2+y^2) 銆倄^2+y^2-a*x=a*sqrt(x^2+y^2)銆2銆鏋佸潗鏍囨柟绋 姘村钩鏂瑰悜: 蟻=a(1-cos胃) 鎴 蟻=a(1+cos胃) (a>0)銆傚瀭鐩存柟鍚: 蟻=a(1-sin胃) 鎴 蟻=a(1+sin胃) (a>0)銆傜畝浠 ...
绛旓細1銆佺洿瑙掑潗鏍囨柟绋 蹇冨舰绾跨殑骞抽潰鐩磋鍧愭爣绯绘柟绋嬭〃杈惧紡鍒嗗埆涓 锛歺^2+y^2+a*x=a*sqrt(x^2+y^2) 锛泋^2+y^2-a*x=a*sqrt(x^2+y^2)銆2銆鏋佸潗鏍囨柟绋 姘村钩鏂瑰悜: 蟻=a(1-cos胃) 鎴 蟻=a(1+cos胃) (a>0)锛涘瀭鐩存柟鍚: 蟻=a(1-sin胃) 鎴 蟻=a(1+sin胃) (a>0)銆
绛旓細鐩磋鍧愭爣鏂圭▼ 蹇冨舰绾跨殑骞抽潰鐩磋鍧愭爣绯绘柟绋嬭〃杈惧紡鍒嗗埆涓 x^2+y^2+a*x=a*sqrt(x^2+y^2) 鍜 x^2+y^2-a*x=a*sqrt(x^2+y^2锛夊弬鏁版柟绋 x=a*(2*cos(t)-cos(2*t))y=a*(2*sin(t)-sin(2*t))鎵鍥撮潰绉负3/2*PI*a^2锛屽舰鎴愮殑寮ч暱涓8a銆鏋佸潗鏍囨柟绋 姘村钩鏂瑰悜锛 蟻=a(1-cos...
绛旓細r=伪锛1-sin 胃锛変负蹇冨舰绾跨殑鏋佸潗鏍囨柟绋銆傚績褰㈢嚎锛屾槸涓涓渾涓婄殑鍥哄畾涓鐐瑰湪瀹冪粫鐫涓庡叾鐩稿垏涓斿崐寰勭浉鍚岀殑鍙﹀涓涓渾鍛ㄦ粴鍔ㄦ椂鎵褰㈡垚鐨勮建杩癸紝鍥犲叾褰㈢姸鍍忓績褰㈣屽緱鍚嶃傚績鑴忕嚎浜︿负铓剁嚎鐨勪竴绉嶃傚湪鏇煎痉鍗氶泦鍚堟涓棿鐨勫浘褰究鏄竴涓績鑴忕嚎銆傚績鑴忕嚎鐨勮嫳鏂囧悕绉扳淐ardioid鈥濇槸 de Castillon 鍦1741骞寸殑銆奝hilosophical...
绛旓細蹇冨舰绾挎瀬鍧愭爣鏂圭▼ 姘村钩鏂瑰悜锛歳=a(1-cos胃) 鎴 r=a(1+cos胃) (a>0)鍨傜洿鏂瑰悜锛 r=a(1-sin胃) 鎴 r=a(1+sin胃) (a>0)鐢ㄥ畾绉垎姹傚績褰㈢嚎闈㈢Н鏃讹紝瀵规按骞虫柟鍚戠殑0鍒跋锛屜鍒2蟺鐨勫浘褰㈠叧浜巟杞村绉帮紝鎵浠ュ彧瑕佹眰涓鍗婄殑闈㈢Н鍐嶄箻浠2銆
绛旓細鏄殑銆傚師鍥狅細蹇冨舰绾挎瀬鍧愭爣鏂圭▼鍨傜洿鏂瑰悜锛 蟻=a(1-sin胃) 鎴 蟻=a(1+sin胃) (a>0)蹇冨舰绾垮湪涓涓渾涓婄殑鍥哄畾涓鐐瑰湪瀹冪粫鐫涓庡叾鐩稿垏涓斿崐寰勭浉鍚岀殑鍙﹀涓涓渾鍛ㄦ粴鍔ㄦ椂鎵褰㈡垚鐨勮建杩癸紝鍥犲叾褰㈢姸鍍忓績褰㈣屽緱鍚嶃傜瑳鍗″皵涔樼Н鍦ㄦ暟瀛︿腑锛屼袱涓泦鍚圶鍜孻鐨勭瑳鍗″皳绉紝鍙堢О鐩寸Н锛岃〃绀轰负X 脳 Y锛岀涓涓璞℃槸X...
绛旓細鍏鏋佸潗鏍囨柟绋涓猴細r=a(1-cos胃)鐢眗^2=x^2+y^2,cos胃=x/r,浠ｅ叆寰楋細鈭(x^2+y^2)=a[1-x/鈭(x^2+y^2)]
绛旓細鍙互鏋佸潗鏍鐨勫舰寮忚〃绀猴細 r =a( 1 - sin 胃)銆鏂圭▼涓合(胃) = a(1 + cos胃)鐨蹇冭剰绾跨殑闈㈢Н涓猴細S=3锛埾a^2锛/2銆傛按骞虫柟鍚戯細r=a(1-cos胃)鎴杛=a(1+cos胃) (a>0)銆傚瀭鐩存柟鍚戯細 r=a(1-sin胃)鎴杛=a(1+sin胃) (a>0)銆傛潵婧愬巻鍙 鍦ㄥ巻鍙蹭笂锛岀瑳鍗″皵鍜屽厠閲屾柉钂傚鐨勭‘鏈夎繃浜ゆ儏锛屼絾...
