

Equation of Tangent to Hyperbola: Preface
A hyperbola is a set of all points (x, y) such that the difference of the distances between (x, y) and two different points is constant. A hyperbola has two vertices that lie on the axis of symmetry known as the transverse axis. The transverse axis of the hyperbola can either be horizontal or vertical. In this article, we will get to know about the different types of equations of the tangent to hyperbola like the equation of tangent of hyperbola in slope form, equation of tangent of hyperbola in parametric form, the chord of contact of hyperbola, and point of contact of the tangent to a hyperbola.
Equation of Hyperbola
The general equation of hyperbola can be represented as

Hyperbola
Point Form Equation of a Tangent to Hyperbola
In this form, the tangent is drawn from the point of contact of the tangent to the hyperbola. Let’s say the point of contact of the hyperbola to tangent is
Equation of Tangent to Hyperbola in Slope Form
This type of equation gives us the equation of the tangent of hyperbola in terms of the slope of the line “m”. The equation is
This equation is also called “The condition of tangency”.
Equation of Pair of Tangents in Hyperbola
When the equation of the hyperbola is
Chord of Contact of Hyperbola
A chord of contact is a chord passing through endpoints of tangents drawn from a point
Equation of Tangent to Hyperbola in Parametric Form
The parametric coordinates of any hyperbola can be represented as
Interesting Facts
When an object, let's say a jet, moves faster than the speed of sound, it creates a conical form of a wave in space and that wave intersects the ground, the curve we get from that intersection is a hyperbola.
The cooling towers are generally made of hyperbolic shape to achieve 2 things: first, the least amount of material used to make it and second, the structure should be strong enough to withstand strong winds.
Solved Examples
Example 1. Find the equation of a tangent to the hyperbola
Solution: Equation of hyperbola :
So ,
The slope of the given line will be
So, the equation of tangent will be
Example 2. Find the equation of the chord of contact of the hyperbola
Solution: We know that The equation of chord of contact of a hyperbola is
Practice Questions
Question 1. What is the value of m for which
Ans:
Question 2. A common tangent to
Ans:
Summary
The article summarises the concept of the chord of contact and tangents as a hyperbola. We learnt about different types of forms of tangents and how to find the equation of these tangents, then we did some examples to brush up on our concepts and get a better understanding of the topic. We hope to have helped you clear your doubts on this topic and learn something new. Do try out the solved examples and practise questions to evaluate your understanding of the concepts discussed here.
FAQs on Various Forms of Tangents in Hyperbola
1. How do you know if a line is a tangent to a hyperbola?
We can know if a line is a tangent to a hyperbola by using the condition of tangency which is
2. What are the parametric coordinates of a hyperbola?
3. What is
In a hyperbola, T is

















