What is equation of director circle of ellipse?

Director circle of ellipse is. x2+y2=a2+b2x2+y2=42.

What is the circle of an ellipse?

A circle is a special case of an ellipse where the two foci or fixed points inside the ellipse are coincident and the eccentricity is zero. In a circle, all the diameters are the same size, but in an ellipse there are major and minor axes which are of different lengths.

What is auxiliary circle in ellipse?

The circumcircle of an ellipse, i.e., the circle whose center concurs with that of the ellipse and whose radius is equal to the ellipse’s semimajor axis.

What is director circle of parabola?

In the conic section, the director circle of a curve is a circle consisting of all points where two perpendicular tangent lines to the curve cross each other. Since a parabola is not a closed curve, the director circle of a parabola is its directrix.

How do you find the director of a circle?

Clearly, x2+y2=50 is the director circle of the circle x2+y2=25.

How do you write the equation of a circle director?

For any general circle whose equation is ${\left( {x – b} \right)^2} + {\left( {y – c} \right)^2} = {r^2}$, the equation of director circle is given by ${\left( {x – b} \right)^2} + {\left( {y – c} \right)^2} = {\left( {\sqrt 2 r} \right)^2}$.

How is ellipse different from circle?

A circle is a closed curved shape that is flat. That is, it exists in two dimensions or on a plane. Ellipses vary in shape from very broad and flat to almost circular, depending on how far away the foci are from each other. If the two foci are on the same spot, the ellipse is a circle.

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.

How do you find the radius of a director of a circle?

The equation of the director circle of a general hyperbola is given by-$x^2 + y^2 = a^2 – b^2$. Comparing it with the general equation of circle we get the radius of the director circle of hyperbola. , where r is the radius. This is the required answer, the correct option is D.

What is the radius of director circle?

How is a circle different from an ellipse?