Prove r = cos (alpha-theta) and r = b sin (alpha-theta) represents two circles intersect orthogonally?
Since α-θ has no real effect on the system let us rewrite this as r = a cosω r = b sinω then converted into Cartesian r ^ 2 = a ^ rr cosω Sinω br 2 = x ^ 2 + y ^ 2 x = ax ^ 2 + y ^ 2 = clearly by one of their intersection is the origin ... the other intersection is (ab ^ 2 / (a ^ 2 + b ^ 2), A ^ 2b / (a ^ 2 + b ^ 2)) we obtain the derivatives of the two curves first curve 2x + 2y dy / dx = a dy / dx = (a - 2x) / ( 2a) (Note that originally, the tangent becomes vertical) Now for the second curve 2x + 2y dy / dx = b dy / dx dy / dx = 2x / (2a - b) (note also at the origin, the tangent is horizontal) we also need to check the tracks on the other point
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Matte Cardstock Stickers: Tiny Circle Alpha/Vintage Navy List Price: $1.75 Sale Price: $1.48 |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Matte Cardstock Stickers: Tiny Circle Alpha/Vintage Black List Price: $1.75 Sale Price: $1.48 |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Matte Cardstock Stickers: Tiny Circle Alpha/Reverse Black List Price: $1.75 Sale Price: $1.48 |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Matte Cardstock Stickers: Tiny Circle Alpha/Reverse Red List Price: $1.75 Sale Price: $1.48 |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Matte Cardstock Stickers: Tiny Circle Alpha/Vintage Red List Price: $1.75 Sale Price: $1.48 |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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Matte Cardstock Stickers: Tiny Circle Alpha/Reverse Brown List Price: $1.75 Sale Price: $1.48 |
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Apothecary Cardstock Stickers. Each of these 7" x 5" sheets features 19 label, journal, border, and shape stickers. Various colors are available (each sold separately). |
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