Shifting of origin

geometry circles coordinate-systems

Find the equation of straight line joining the point $(2,2)$ to the points in which the straight line $y=mx+c$ cuts the circle, $x^2 + y^2 =2ax+2ay$. Hence find the condition that these points may subtend a right angle at the point $(2,2)$. I am sure if the point in the question were to be origin, I could use homogenization to solve the problem, So I wanted to ask to solve this problem should I shift the origin from $(2,2)$ to $(0,0)$ like changing the equations to $(y-2)=m(x-2)$ and $(x-2)^2+(y-2)^2=2a(x-2)(y-2)$ and the solve the question?

Please let me know if my method is correct


Solution 1:

Hint: To shift $(2,2)$ to the origin, remember that $x=(x+2)-2$ and $y=(y+2)-2$ shift

Related

Finding area between a curve and a line using double integrals?
Curves in $\mathbb{R} ^3 $ [duplicate]
Components in the complement of compact subset in manifold
Is the kth central moment less than the kth raw moment for even k?
The equation $y = x^2 + \frac{1}{2}ax + a$ represents a parabola for all real values of $a$ [closed]
$f, g:[a, b] \rightarrow [a, b] $ be any two continuous functions $(a, b \in \Bbb{R}) $ such that $\inf f(x) =\inf g(x) $
How to incrementally sample without replacement?
tail -f in python with no time.sleep
Is there any standard way of embedding resources into Linux executable image? [duplicate]
Remove duplicate items from an array [duplicate]
How to list branches that contain an equivalent commit
Reading and writing a std::vector into a file correctly