Articles of tangent line

Finding the tangent of an ellipse that is perpendicular to a line

The books say’s “Find the equations of the tangents to $x^2+3y^2=4$ which are perpendicular to the line $x-2y=7$“ I’ve graphed them and found that the given line does not pass through the ellipse and the gradient of the tangent should be $dy/dx=-x/3y$. I don’t know how to get an expression for the tangent because all […]

To draw a straight line tangent to two given ellipses.

How can I draw a a straight line that touches two ellipses? There are, like for two circles, 4 different solutions. I am not interested in the analytical solution, but in the geometrical drawing, although no matter if conics appear. Thanks.

Find a line which is tangent to the curve $y=x^4-4x^3$ at 2 points

How can I solve this? Should I set the two points as $a^4-4a^3$ and $b^4-4b^3$?

Problem with basic definition of a tangent line.

I have just started studying calculus for the first time, and here I see something called a tangent. They say, a tangent is a line that cuts a curve at exactly one point. But there are a lot of lines that can cut the same point just like shown in the picture- WHY aren’t we […]

Minimum operations to find tangent to circle

I’ve been playing the game Euclidea 3, and I can’t really wrap my mind around one of the minimal solutions: The object is to get a tangent line on right of the blue circle with only 3 operations. The minimum solution involves only 2 compass operations (shown above as the gray circles) and the final […]