What is the equation of director circle of hyperbola?

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.

How do you find the director of a circle?

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

What is the Auxiliary circle of an 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 derive the equation of a circle director?

The required equation of the director circle is obtained by finding the radius of the given circle and then multiplying it with $\sqrt 2 $ in order to get the radius of the director circle.

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

1. The radius of director circle of hyperbola is a2x2​−b2y2​=1. Medium.
2. The radius of director circle of the hyperbola 16×2​−9y2​=1 is.
3. The equation of director circle of hyperbola is 36×2​−25y2​=1 is.
4. The diametre of director circle of hyperbola 25×2​−16y2​=1.
5. The equation of director circle of hyperbola a2x2​−b2y2​=1 is.

How do you find the equation of the auxiliary circle?

Note: A circle drawn with center O and $P1P$ as diameter is called the auxiliary circle of the hyperbola. Equation of the auxiliary circle of a hyperbola is ${x^2} + {y^2} = {a^2}$.

How do you find the Auxiliary circle of an ellipse?

1. The circle having major axis of the ellipse as diameter is called as the auxiliary circle of the ellipse.
2. If the equation of the ellipse is x^2/a^2 + y^2/b^2 = 1 where the length of major axis is 2a,
3. the equation of the auxiliary circle is x^2 + y^2 = a^2.

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 of an ellipse?

What is auxiliary circle in ellipse?

How do you find the director circle of an ellipse?

⇒ The radius of the director circle is a 2 + b 2. x 2 + y 2 = a 2 + b 2. In case the centre of the ellipse is not at the origin but is at ( h, k), then the equation of the director circle of an ellipse would be ( x − h) 2 + ( y − k) 2 = a 2 + b 2. Is a director circle of a parabola possible?

What is a director circle in math?

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 an ellipse?

In your case, the ellipse is actually a circle with the equation x²+y²=36. So the center is at the origin and the radius is 6. Draw a rectangle around your ellipse. (a square in this case) The corners of this square will touch the sides of the Director circle.

What is the equation of the director circle of y2b2 = 1?

Equations of director circle of— y2b2 = 1 is x2 + y2 = a2 + b2 .The length of latus rectum in (i) parabola is 4a; (ii) ellipse and hyperbola is 2bVa. 5. The equation of the director circle is Ii) Ellipse is : x2 + y2 = a2 + b2