Intersection point between a line and an ellipse

This time, I have been trying to find the equation of intersection point between line and ellipse. I wrote an equation but the delta is negative so I can`t find the roots.

x,y is the intersection point,
x1, y1 is the start point of the line
h, k is the center point of the line
a is the major radius of the ellipse lies on X axis
b is the minor radius of the ellipse lies on Y axis

m = tan(AngleOfLine)

(y - y1) = m * (x - x1) -> y = m * (x - x1) + y1

I put m * (x - x1) + y1 instead of y in the ellipse equation
(x - h) ^ 2 / a ^ 2 + (y- k) ^ 2 / b ^ 2 = 1

and tried to solve.
After I opened all of the paranthesises (very long line) and converted the equation in ax^2 + bx + c = 0 form, but the delta is negative.

Even I tried to resolve this equation, the result is the same. I`m not sure if I`m doing something wrong but it seems right.

Would you please help me to find that intersection point?
Thanks in advance.

either the line does not intersect the elipse or double check your arithmetic.

Thanks for your reply bugzpodder.
I have checked the equation 5 times, but everything is the same.
I formed the equation in ax^2 + bx + c = 0 . I give a , b and c below.

x1, y1 : coords of startpoint of the line
x, y : coords of the intersection point
h, k : coords of the center point of the ellipse
ax, bx are major radius and minor radius of the ellipse.

m = tan(Angle of the line)

a = bx ^ 2 + (ax ^ 2 * m ^ 2)

b = -2 * (bx ^ 2 * h + ax ^ 2 * m ^ 2 * x1 - ax ^ 2 * m * y1 + ax ^2 * k * m)

c = bx ^ 2 * h ^ 2 + ax ^ 2 * m ^ 2 * x1 ^ 2 - ax ^ 2 * 2 * m * y1 * x1 + ax ^ 2 * y ^ 2 + ax ^ 2 * 2 * k * m * x1 - ax ^ 2 * 2 * k * y1 + k ^ 2 * ax ^ 2 - ax ^ 2 * bx ^ 2

(-b - squareroot(b ^ 2 - 4 * a *c)) / 2a
(-b + squareroot(b ^ 2 - 4 * a *c)) / 2a

both must give the two x values of the intersection point but delta is negaive.

I graphically tested the coordinates of the ellipse and line with AutoCAD, and the line intersected with the ellipse. But the equation above didn`t give the coords of the intersection point with the same parameters.

Would you please help?

since you said ur able to draw it in autocad, i assume u have numeric numbers instead of a,b,c,d,e. y don't you give me that instead of a mess of equations?

I attached the drawing.

h,k : 200, 100
major radius = ax = 100
minor radius = bx = 50

x1, y1 = 275, 150
m = tan(21,80140949)

So,

a = 50 ^ 2 + (100 ^ 2 * m ^ 2) = 2868,82928182602

b = -2 * (50 ^ 2 * 200 + 100 ^ 2 * m ^ 2 * 275 - 100 ^ 2 * m* 150 + 100 ^ 2 * 100 * m)= -1394905,39082075

c = ... = 180706268,037612

delta = b ^ 2 - 4 * a * c = -127900683282,42152740697049446

I`m very sorry mate, for taking your time. Please excuise me.
I find the mistake: I have these equations solved by converting them to code in C++ and I forget tan(x) function gets the x in radians and I have entered it in degrees.
I had been working on this for days just because a simple mistake.

I apologize everyone who even read this post.