A level maths question about tangents

I was wondering if you can always set the discriminant=0 for a tangent to a curve if you have a quadratic in x. surely you cant always do this since you can have a tangent to a curve at one point which then intersects with the curve at another point so there would be 2 solutions for x, no?

I was wondering if you can always set the discriminant=0 for a tangent to a curve if you have a quadratic in x. surely you cant always do this since you can have a tangent to a curve at one point which then intersects with the curve at another point so there would be 2 solutions for x, no?

How can a tangent to a quadratic intersect the curve again? You might need to show a picture of what you mean.

A tangent can't intersect a quadratic curve, because that is a line that would go through two points of the curve. That is not the case for a tangent. A tangent touches the curve on a certain point, that's it. But a secant can do this.

Would be nice, when you send the question paper to it for a better understanding of the excercise.

I dont necessarily mean a quadratic curve but moreso just a curve/function which you can get into the form of a quadratic when finding it's intersection with a line.

The reason I asked was because i was looking at a maths question where you had a hyperbola and needed to simplify the equation of a tangent and the solution back plugged y=mx+c into the general hyperbola question, expanded, then set the descriminant=0

Best to post the actual question/solution so as to be clear what you're talking about.

But guessing: A tangent to an hyperbola will only touch the curve once (and not intersect/touch it again). So, if the x-coordinates of the point of intersection are the subject of a quadratic equation, then for a tangent, it can have only one, repeated root , and hence the discriminant must be 0.

Keypoints: The tangent can only touch/intersect the curve once, and you get a quadratic for its x-coordinate. Think this is true of any conic section.

Agree. Thinking about the asymptotes make it reaonably clear.
https://plus.maths.org/content/meet-hyperbola

Best to post the actual question/solution so as to be clear what you're talking about.

But guessing: A tangent to an hyperbola will only touch the curve once (and not intersect/touch it again). So, if the x-coordinates of the point of intersection are the subject of a quadratic equation, then for a tangent, it can have only one, repeated root , and hence the discriminant must be 0.

Keypoints: The tangent can only touch/intersect the curve once, and you get a quadratic for its x-coordinate. Think this is true of any conic section. Edit: Certainly for a hyperbola or parabola.