Director Circle

x ^(2) +y ^(2) =a ^(2) is the standard equation of a circle centred at (0,0) and radius is a. Paramatric Equation to Standard Circle: Parametric Equation for the circle x^(2) +y ^(2) =a ^(2) is x =a cos theta, y =a sin theta. Director Circle: Director circle is the locus of point of intersection of two perpendicular tangents. Two points A (-30^(@)) and B (150^(@)) lies on circle x ^(2) +y ^(2) =9. The point (theta) which moves on a circle such that area of Delta PAB is maximum, is/are

x ^(2) +y ^(2) =a ^(2) is the standard equation of a circle centred at (0,0) and radius is a. Paramatric Equation to Standard Circle: Parametric Equation for the circle x^(2) +y ^(2) =a ^(2) is x =a cos theta, y =a sin theta. Director Circle: Director circle is the locus of point of intersection of two perpendicular tangents. A ray of light which comes from (-3,1) travels along a line L and after reflection from the circle x ^(2) +y ^(2) =a ^(2), reficated ray moves along the same line L, then the equation of line L is

Q.14 lfe is eliminated from the equations a sec e-xtan e- y and b sec 0+ y tan ex (a and b are constant) then the eliminant denotes the equation of (A) the director circle ofthe hyperbola xr- (B) auxiliary circle of the ellipse +2 1 (C) Director circle of the ellipse (D) Director circle of the circle x t y?

A circle x^(2)+y^(2)+4x-2sqrt(2)y+c=0 is the director circle of the circle S_(1) and S_(1) is the director circle of circle S_(2), and so on.If the sum of radii of all these circles is 2 ,then the value of c is k sqrt(2), where the value of k is

A circle S of radius 'a' is the director circle of another circle S_(1),S_(1) is the director circle of circle S_(2) and so on.If the sum of the radii of all these circle is 2, then the value of 'a' is 2+sqrt(2)(b)2-(1)/(sqrt(2))2-sqrt(2)(d)2+(1)/(sqrt(2))

If the foci of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 coincide with the foci of (x^(2))/(25)+(y^(2))/(9)=1 and the eccentricity of the hyperbola is 2, then a^(2)+b^(2)=16 there is no director circle to the hyperbola the center of the director circle is (0,0). the length of latus rectum of the hyperbola is 12

A circle S=0 passes through the common points of family of circles x^(2)+y^(2)+lambda x-4y+3=0 and (lambda varepsilon R) has minimum area then (A) area of S=0 is pi sq. units (C) radius of director circle of S=0 is 1 unit (D) S=0 never cuts |2x|=1 (B) radius of director circle of S=0 is sqrt(2)

If C_(1): x^(2)+y^(2) =(3+2sqrt(2))^(2) be a circle. PA and PB are pair of tangents on C_(1) where P is any point on the director circle of C_(1) , then the radius of the smallest circle which touches C_(1) externally and also the two tangents PA and PB is