0
votes
1answer
45 views

maximum radius of a circle inscribed in an ellipse

Consider an ellipse with major and minor axes of length 10 and 8 resp. The radius of the largest circle that can be inscribed in this ellipse, given that the centre of this circle is one of the focus ...
3
votes
3answers
260 views

What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
0
votes
1answer
194 views

What are the coordinates of the ends of the latus rectum of the parabola $x^2 - 2y + 2 = 0$? [duplicate]

I've already graphed the parabola . i just don't know how to locate it's focus and the ends of it's latus rectum. On my graph, the vertex is on (0,1). Please help me with this. ASAP.
2
votes
1answer
78 views

Coordinate System Rotation and Cross Term

If I have a conic equation $$ 5x^2 - 4xy + 8y^2 = 36 $$ and $ \left[\begin{array}{cc} 5 & -2\\ -2 & 8 \end{array}\right] $ in matrix form, whose eigenvalues are 4 and 9, how would I rotate ...
1
vote
1answer
3k views

How to find equation of parabola when we only know the equation of latus rectum and coordinates of vertex?

Suppose the equation of latus rectum is x=4 and the vertex is (2,3). I am confused wouldn't there be many parabola with this same vertex and latus rectum.If not how to find the equation? The answer ...
2
votes
3answers
74 views

Find at least two ways to find $a, b$ and $c$ in the parabola equation

I've been fighting with this problem for some hours now, and i decided to ask the clever people on this website. The parabola with the equation $y=ax^2+bx+c$ goes through the points $P, Q$ and $R$. ...
2
votes
1answer
190 views

How to find the eccentricity of this conic?

How to find the eccentricity of this conic? 4(2y-x-3)² - 9(2x+y-1)²=80 My approach : I rearranged the terms and by comparing it with general equation of 2nd degree, I found that its a hyperbola. ...
0
votes
1answer
129 views

How to “transform” $(f(x), g(x))$ to $(x, y(x))$?

I'm currently trying to solve the following problem: Let $L$ be the set of points of $\mathbb{R}^2$ that satisfy the condition $f(x,y) = 7x^2-6 \sqrt{3} xy + 13y^2 = 16$. It is possible to ...
0
votes
2answers
863 views

Plot ellipse in cartesian coordinates

I am working with a computer program that needs to draw objects in a 3d field. Over time, these objects will move (at different rates) on an elliptical path around the 0,0,0 point. I've read the ...