Need help on an equation of tangent lines

In summary, the conversation discusses finding the equation of the set of all points from which the two tangents to an ellipse are perpendicular. The approach of finding the slope of the equation and using the concept of perpendicular lines is mentioned, but the specific steps are still unclear. The question also raises the point that the points in question are not on the ellipse and prompts the consideration of the equations of the tangent lines and the condition for them to be perpendicular.
  • #1
kevinchhan
1
0
Having trouble with this:

Given an ellipse (x^2/a^2) + (y^2/b^2) = , a!=b. Find the equation of the set of all points from which the two tangents to the curve are perpendicular.

I tried finding the slope of the equation then knowing that perpendicular line are the opposite reciprocal. But still clueless on how to put it together.

Thanks in advance
 
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  • #2
The points in question are not on the ellipse. Suppose [itex](x_0, y_0)[/itex] is a point not on the ellipse. Then there are two lines tangent to the ellipse through [itex](x_0, y_0)[/itex]. What are there equations? What must be true if those two lines are perpendicular?
 

FAQ: Need help on an equation of tangent lines

What is an equation of tangent lines?

An equation of tangent lines is a mathematical expression that represents a straight line that touches a curve at a specific point, without crossing or intersecting it. It is used to find the slope or rate of change of a curve at a given point.

How do you find the equation of tangent lines?

To find the equation of tangent lines, you need to know the coordinates of the point where the tangent line touches the curve. Then, you can use the slope formula or the derivative of the curve to calculate the slope of the tangent line. Finally, you can use the point-slope form or the slope-intercept form to write the equation of the tangent line.

What is the point-slope form of the equation of tangent lines?

The point-slope form of the equation of tangent lines is y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line. This form is useful when you know the coordinates of the point of tangency and the slope of the tangent line.

How do you use the slope-intercept form to write the equation of tangent lines?

The slope-intercept form of the equation of tangent lines is y = mx + b, where m is the slope of the tangent line and b is the y-intercept. This form is useful when you know the slope of the tangent line and the y-intercept, which can be calculated by substituting the coordinates of the point of tangency into the equation y = mx + b.

Can the equation of tangent lines be used for any curve?

Yes, the equation of tangent lines can be used for any curve, as long as the curve is differentiable at the point of tangency. This means that the curve must have a well-defined slope at that point. If the curve is not differentiable, the equation of tangent lines cannot be used.

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