Linked Questions
13 questions linked to/from The locus of the intersection point of two perpendicular tangents to a given ellipse
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Orthogonal tangents to an ellipse [duplicate]
This is the problem I found back in the first year in the university.
Suppose we have a non-degenerate (i.e. not a point and not an empty set) ellipse $E\subset \Bbb R^2$. Now define a set $D$ by a ...
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Given an ellipse, find the equation of the set of all points from which there are two tangents to the curve whose slopes are reciprocal. [duplicate]
Given an ellipse $x^2/a^2+y^2/b^2=1,$ where $a\not=b,$ find the equation of the set of all points from which there are two tangents to the curve whose slopes are (a) reciprocals and (b) negative ...
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Finding formula of all solution of a point P, where two tangent line to an ellipse from P is perpendicular to each other [duplicate]
the only information given is ellipse equation x^2/17+y^2/8=1, first I tried to substitute y in ellipse equation with m(x-a)+b, then I tried to make determinant zero, getting 2nd order equation of am^...
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How to get the limits of rotated ellipse?
The box that an ellipse fits is easily calculated if there are no rotation, or if the rotation is ${x*90^o}$ (where x is an integer) is easy.
For a (major radius) and b (minor radius), it is :
<...
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How to calculate width and height of a 45° rotated ellipse bounded by a square?
I'm coming from a programming background so I apologies if this is blindingly simple or I misuse terms. I have an ellipse bounded by a square. For simplicity the centre of the square and ellipse is ...
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Finding the locus of a point $P$ if the tangents drawn from $P$ to circle $x^2 + y^2 = a^2$ so that the tangents are perpendicular to each other?
Question: Find the locus of a point $P$ if the tangents drawn from $P$ to circle $x^2 + y^2 = a^2$ so that the tangents are perpendicular to each other.
I tried solving this and then I got to this ...
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Rectangle circumscribed to an ellipse of max area/perimeter
I could solve the classical problem of maximizing the area (fixing the perimeter) or maximizing the perimeter (fixing the area) of an inscribed rectangle, but I don't know how to solve ...
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2
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Relation of ellipse semi-axes with rotation angle and projection length
In the following setup, assume $w$ (length of the projection of the ellipse) and $\theta$ (the rotation angle) are known. I want to know what equation(s) do I have here that helps me to derive the ...
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Can a figure inside a circle be seen at right angle from any point on the circle?
A convex, closed figure lies inside a given circle. The figure is seen from every point of the circumference at a right angle (that is, the two rays drawn from the point and supporting the convex ...
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Find the number of points on ellipse $\frac{x^2}{50}+\frac{y^2}{20}=1$ from which pair of perpendicular...
Find the number of points on ellipse $\frac{x^2}{50}+\frac{y^2}{20}=1$ from which pair of perpendicular tangents are drawn to ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$
Normal from a point $(5\sqrt{2}...
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how to obtain peripheral recangle of arbitrary ellipse?
Suppose have arbitrary ellipse with center $(x,y)$ and its radius $(a,b)$. I want obtain rectangle that sides tangent of peripheral ellipse. the below image describe issue :
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1
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Set of points from which tangent lines to given hyperbola are perpendicular.
Find set of points from which start two perpendicular tangent lines to hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$
Tangent lines to a hyperbola are $y=mx+\sqrt{a^2m^2-b^2}$ and $y=mx-\sqrt{a^2m^2-...
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$\alpha$-isoptic curve of a conic section
Could someone tell me where I can find the generic equation of the $\alpha$-isoptic of a conic section of this form:
$$\Gamma: ax^2+2bxy+cy^2+2dx+2ey+f=0$$
I searched in many links and PDFs but I ...
