Table of Contents

## Are tangents to ellipse perpendicular?

That is, at every point on the (upper half of the) circle, the two lines through the point that are tangent to the ellipse are perpendicular to each other. So all such points are on the circle, and all points on the circle are such points. (The circle is called the director circle of the ellipse).

### How is a tangent drawn from a point on the ellipse?

Tangents are drawn from a point P(6,sqrt(5)) to the ellipse x^2/25+y^2/16=1touching the ellipse in the points Q and R. The angle between PQ and PR is. Equation of tangent to an ellipse=>y=mx±√a2m2+b2.

**How many perpendicular tangents can be drawn to a hyperbola?**

Statement–1 : There can be infinite points from where we can draw two mutually perpendicular tangents on to the hyperbola.

**How do you find the point of contact between tangent and ellipse?**

Point of contact of the tangent to an ellipse Line y = mx ∓ √[a2m2 + b2] touches the ellipse x2 / a2 + y2 / b2 = 1 at (∓a2m / √[a2m2 + b2]) , (∓b2 / √[a2m2 + b2]).

## What is the focal distance of an ellipse?

What is the focal distance of a point on the ellipse? The sum of the focal distance of any point on an ellipse is constant and equal to the length of the major axis of the ellipse. Let P (x, y) be any point on the ellipse x2a2 + y2b2 = 1. Therefore, SP + S’P = a – ex + a + ex = 2a = major axis.

### How do you find the chord length of a contact?

Chord length = 2√r2-d2 , where r is the radius of the circle and d is the perpendicular distance of the center of the circle to the chord.

**What is the meaning of Director circle?**

In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross each other.

**At what point is the tangent line to perpendicular to the line?**

The derivative of a function at a point is the slope of the tangent line at this point. The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency.

## How many perpendicular tangents can a circle have?

Hint: Only one tangent can be drawn to a circle from a point on the same circle, we will prove this by constructing a line perpendicular to the radius and will prove that all other points of the line lie exterior of the circle and hence touches the circle at a single point.