Mathematics
Mathematics
Problem
If the line touches the ellipse , then find the point of contact.Intuitive explanation
A line is tangent to an ellipse when it touches at exactly one point—which means the system of the line and ellipse equations has exactly one solution. Substitute the line equation into the ellipse to get a quadratic in one variable; when the discriminant equals zero, you've found the tangency condition. That single solution is your point of contact.
Intuitive explanation
A line is tangent to an ellipse when it touches at exactly one point—which means the system of the line and ellipse equations has exactly one solution. Substitute the line equation into the ellipse to get a quadratic in one variable; when the discriminant equals zero, you've found the tangency condition. That single solution is your point of contact.