Inclined Ellipse Intersection

[msk2015]

I have a ellipse with center (h , v) , Radius a and b , angle of inclination Theta.

I have a point P (x1 , y1) either inside or outside ellipse. I need to find the point

of intersection Q (x , y) of inclined ellipse and line passing through ellipse center and point P.


I need formula to find Q (x , y)



I have two equations y1 = m x1 ; m = y1/ x1

Equation of Inclined Ellipse : (xcos(theta) + ysin(theta)) ^ 2 / a ^2 + ( x sin(theta) - ycos(theta)) ^2 / b ^2 = 1;

I replaced value of y by mx1 and tried to solve.

I failed . Pl help me .. are my formulae correct ? How to find roots ?

 

[stapel]

By "Radius a and b", do you maybe mean "semi-minor and -major axis lengths of a and b"? Thank you!

 

[msk2015]

By "Radius a and b", do you maybe mean "semi-minor and -major axis lengths of a and b"? Thank you!

Stapel sir , radius_a and radius_b means a and b ... Thank u .. pl help to solve the equation

 

[msk2015]

Stapel Sir , sorry for using shortforms ..

I am trying to write my difficulty again with clarity ..


I have an Ellipse with Center Point C(h,k) , Radius_a as Semi Major Radius , Radius_b as semi minor radius b and
Angle Ang as angle of Inclination

There is point P (x1 , y1) can be inside the ellipse or outside the ellipse. A line connects Point P and Center of Ellipse Point C.
So the LIne PC intersects an Ellipse at point Q(X,Y) . I need the formula to get Coordinates of point Q.

I have Ellipse Equation with respect to point Q as (xcos(Ang)+ycos(Ang)^2 / Radius_a^2 + (xsin(Ang)-ycos(Ang)^2 / Radius_b^2 = 1;

Considering Line CQ I have another equation y = mx ; where m = y/x;

I failed to solve these equations to find Q(x,y);

Will you please help ?

Thanking you ...