Tangent Properties and Intersections

The video tutorial explores the properties and equations of tangents, focusing on their intersections and the concept of perpendicular tangents. It delves into the relationship between tangents, focal chords, and the directrix, providing insights into their mathematical significance.

What is the gradient of a tangent at a point P?

• The value of P

• The x-coordinate of P

• The y-coordinate of P

• The square of P

What is the y-intercept of a tangent at point P?

• It is zero

• It corresponds to the y-coordinate of P

• It is the x-coordinate of P

• It is the negative of the x-coordinate of P

What is the first step in finding where two tangents intersect?

• Solve the equations simultaneously

• Multiply the equations of the tangents

• Subtract the equations of the tangents

• Add the equations of the tangents

When solving for the intersection of two tangents, what is eliminated from the equations?

• The gradient

• The constant term

• The y-coordinate

• The x-coordinate

What mathematical operation is used to simplify the intersection equations?

• Subtraction

• Integration

• Addition

• Factorization

What is the result when the gradients of two tangents are multiplied?

• Zero

• One

• Minus one

• Infinity

What does it mean if the gradients of two tangents multiply to minus one?

• The tangents do not intersect

• The tangents are identical

• The tangents are perpendicular

• The tangents are parallel

What is the significance of a focal chord in relation to tangents?

• It is the line where tangents intersect perpendicularly

• It is the line where tangents are parallel

• It is the line where tangents do not intersect

• It is the midpoint of the tangents

What is the alternative definition of the directrix?

• The line where tangents do not intersect

• The midpoint of the parabola

• The locus of points traced by tangent intersections

• The line where tangents are parallel

What is the visual representation of the intersection of tangents?

• A parabola

• A circle

• A triangle

• A straight line