Pedal curves

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Problem 1981 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

The pedal curve of a curve with respect to a given point is the locus of the feet of perpendiculars dropped from the given point onto the tangents to the given curve. Find the pedal curve of the ellipse $\dfrac {x^{2}}{a^{2}}+\dfrac {y^{2}}{b^{2}}=1$ with respect to the center.

Problem 1982 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the parabola $y^{2}=2px$ with respect to the vertex.

Problem 1983 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the parabola $y^{2}=2px$ with respect to the focus.

Problem 1984 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the hyperbola $x^{2}-y^{2}=a^{2}$ with respect to the origin.

Problem 1985 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the curve $\left(\dfrac {x}{a}\right)^{n}\pm \left(\dfrac {y}{b}\right)^{n}=1$ with respect to the point $(0,0)$ .

Problem 1986 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the curve $r=e^{a\varphi }$ with respect to the pole.

Problem 1987 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the curve $x^{2}+y^{2}=2ax$ with respect to the point $(0,0)$ (give the answer in polar coordinates).

Problem 1988 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the curve $r^{n}=a^{n}\cos n\varphi$ with respect to the pole.

Problem 1989 from Гюнтер Н.М., Кузьмин Р.О. "Сборник задач по высшей математике" [ГюКу03]More problems in Section 5.2 "The Tangent and the Normal"

Find the pedal curve of the involute of a circle:

x = a(\cos t+t\sin t), \qquad y = a(\sin t-t\cos t)

with respect to the origin.

References

[ГюКу03] Гюнтер Н.М., Кузьмин Р.О. Сборник задач по высшей математике. 13-е изд., Издательство «Лань», 2003.