All Questions
Tagged with circles conic-sections
221
questions
1
vote
1
answer
43
views
Circles,projectile motion and parabola
Q) A projectile is thrown at an angle theta from O(0,0) and reaches R(R,0) given R is the range of projectile
A point P is taken on its trajectory and is joined with O(0,0) and R(R,0) such that angle ...
0
votes
1
answer
79
views
From a physics textbook: how did they get the eccentric anomaly ψ?
The initial formula was:
$$
\begin{align}
\cos\psi &= \cos(θ-θ₀) + e \sin^2(θ-θ₀) - e^2 \cos(θ-θ₀)\sin^2(θ-θ₀)\\
&+ e^3 \cos^2(θ-θ₀)\sin^2(θ-θ₀) - ...\\
\end{align}
$$
Where e is the ...
2
votes
1
answer
55
views
Determine the circle that is tangent to three given ellipses
Given three ellipses in the plane specified as follows
$(r - C_1)^T Q_1 (r - C_1) = 1$,
$(r - C_2)^T Q_2 (r - C_2) = 1$
$(r - C_3)^T Q_3 (r - C_3) = 1$
I want to find the circle that is externally ...
- 24.2k
0
votes
1
answer
218
views
Why is there no $\pi$ in an ellipse?
Allow me to clarify ...
With a circle of circumference $c$ and diameter $d$, $\pi$ makes an appearance as $\frac{c}{d}$ even though the equation of a circle, $(x - h)^2 + (y - k)^2 = r^2$, doesn't ...
- 967
6
votes
2
answers
273
views
Circle tangent to rotated ellipse and horizontal line
I would like to find the position for the center of a circle $(x_0, y_0)$ that is tangent to both an ellipse and a horizontal line.
The ellipse is positioned at $(0,0)$ and is defined by major axis $a$...
- 71
0
votes
0
answers
47
views
Generalizing circles passing through two points
You can easily construct a circle which has $A=(0, 0)$ as its center and two points $B$, $C$ of the same distance to $A=(0, 0)$ being located on it:
I wonder if it is possible to have an ellipse ...
- 133
2
votes
1
answer
92
views
Equations of possible common tangential planes to two circles in 3-space.
This is similar to the question posed here, but I am interested in the case of two circles $C_1$ and $C_2$ of different radii $r_1$ and $r_2$, sharing a common tangent. The circles are not co-planar. ...
- 2,948
5
votes
2
answers
361
views
Circle tangent to ellipse
A small circle is tangent to the lower right quarter of a larger ellipse. The ellipse is straight (not rotated), and its lowest point is centered at origo.
The following is given:
"a", the ...
- 53
1
vote
1
answer
81
views
circumcircle equation
Circle $x^2+y^2=9$ and parabola $y^2=8x$.
They intersect at P and Q. Tangents to the circle at P and Q meet x-axis at R and tangents to the parabola at P and Q meet the x-axis at S.
On solving we get ...
- 469
0
votes
2
answers
183
views
Intersection of circle and parabola and quadratic discriminant
Circle $x^2+y^2=9$ and parabola $y^2=8x$
They intersect at two points and at the same x-coordinate. On solving we get a quadratic equation in x as $x^2+8x-9=0$. It should give one value of x, hence ...
- 469
0
votes
2
answers
517
views
Question on rectangular hyperbola and its focus and directrix.
Let S be the focus of the hyperbola $xy=1$. Let a tangent to the hyperbola at point P cuts the latus rectum (through S) produced, at point Q and the directrix (corresponding to S) at point T. Also let ...
- 8,318
1
vote
2
answers
739
views
Find the shortest distance between the circle $x^2+y^2-24x+128=0$ and the curve given by the locus of P.
Four normals are drawn to the rectangular hyperbola $xy=c^2$ from a point $P(h,k)$. Find the shortest distance between the circle $x^2+y^2-24x+128=0$ and the curve given by the locus of P.
My Attempt:...
- 8,318
0
votes
1
answer
53
views
Point of intersection of two circles with center of one circle lying on another circle
Consider the following configuration:
Two circles with center R and S are shown.Now, suppose I know point R and S and let the radius of both circles be $r_1$ and $r_2$. I need to find point V and U.
...
- 415
1
vote
1
answer
474
views
Show that the feet of the normals from the point ($\alpha,\beta,\gamma$) to the paraboloid $x^2+y^2=2az$ lie on a sphere
Show that the feet of the normals from the point ($\alpha,\beta,\gamma$) to the paraboloid $x^2+y^2=2az$ lie on the sphere $y^2+x^2+z^2-z(\alpha+\gamma)-\frac{y}{2\beta}(\alpha^2+\beta^2) = 0$, when $\...
- 103
2
votes
0
answers
119
views
The radius of the circle which touches the line $x +y = 0$ at $M(-1,1)$ and cuts the circle $\ x^2+y^2+6x-4y+18=0 $ orthogonally is?
I had attempted the question using the formula :
$$\ r_1^2 + r_2^2 = d^2 $$
But when I tried to find the radius by the first formula i got the radius as $\sqrt -5$
Then I got confused how can a "...
- 59