The discussion focuses on finding the equations of the tangents to the ellipse defined by the equation 4x² + 9y² = 36, which are equally inclined to the x and y axes. The solution involves substituting y = mx + c into the ellipse equation and analyzing the quadratic discriminant, leading to the conclusion that c² = 9m² + 4. It is established that "equally inclined" implies the slopes of the tangent lines must be ±1, confirming the need for calculus methods in the solution.
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Doesn't "equally inclined" to the x and y axes mean that the slopes of the tangent lines have to be 1 or -1?sooyong94 said:Homework Statement
Find the equation of the tangents to the ellipse 4x^2+9y^2 = 36 which are equally inclined to the x and y-axis.
Homework Equations
Quadratic discriminant
The Attempt at a Solution
First I substituted y=mx+c into the ellipse, and determined its discriminant, and got c^2 = 9m^2 + 4