Equally inclined tangents of an ellipse

In summary, the problem is to find the equation of tangents to the ellipse 4x^2+9y^2 = 36 that are equally inclined to the x and y-axis. This involves substituting y=mx+c into the ellipse and using the quadratic discriminant to find c^2 = 9m^2 + 4. The slopes of the tangent lines are required to be 1 or -1, making this a calculus problem.
  • #1
sooyong94
173
2

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
 
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  • #2
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
Doesn't "equally inclined" to the x and y axes mean that the slopes of the tangent lines have to be 1 or -1?

Also, I'm reasonably sure that this is a calculus problem, so it should not be posted in the Precalc section. I'm moving it to the Calc & Beyond section.
 

Related to Equally inclined tangents of an ellipse

What is an equally inclined tangent of an ellipse?

An equally inclined tangent of an ellipse is a line that intersects the ellipse at two points, making equal angles with the tangent line at those points. This line divides the ellipse into two symmetrical halves.

How many equally inclined tangents does an ellipse have?

An ellipse has an infinite number of equally inclined tangents, as there are an infinite number of possible angles that can be formed with the tangent line at any given point on the ellipse.

What is the significance of equally inclined tangents in an ellipse?

Equally inclined tangents in an ellipse are important because they help to define the symmetry of the shape. They also play a role in determining the orientation and position of the ellipse in relation to other objects or shapes.

How can equally inclined tangents be calculated?

The equation for an ellipse can be used to calculate the coordinates of points on the curve. By finding the slope of the tangent line at two points on the ellipse and setting those slopes equal to each other, the coordinates of the equally inclined tangent line can be determined.

What other properties are associated with equally inclined tangents in an ellipse?

Equally inclined tangents are also associated with the concept of conjugate diameters in an ellipse, which are two diameters that intersect at the center of the ellipse and form equal angles with the tangent lines at their points of intersection.

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