Circles, Mathematics

If the distances from origin of the centres of 3 circles x2+y2+2alphaix= a2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+y2 = a2 are in :

(a) A.P (b) G.P (c) H.P (d) None of these


Ans)   C

centres of the 3 circles are (-alphai,0) (i= 1,2,3)

Distances of thes from origin are alpha1, alpha2, alpha 3

now (alpha2)^2= (alpha1)(alpha3)

Also general point on  x2+y2=a2 is (a costheta, a sintheta) length of tangent from this point on the given circle is

sqrt( (a cos theta)2+(a sintheta)2 +2alphai(a costheta) -a2)) = sqrt ( 2alphai(a costheta))

now as alpha 1, alpha 2, alpha 3 are in GP

then sqrt alpha 1, sqrt alpha 2, sqrt alpha 3 are in gp

then sqrt 2acos theta alpha 1 , 2acos theta alpha 2 and sqrt 2acos theta alpha 3 are also in GP

Posted Date: 3/11/2013 7:33:13 AM | Location : United States







Related Discussions:- Circles, Assignment Help, Ask Question on Circles, Get Answer, Expert's Help, Circles Discussions

Write discussion on Circles
Your posts are moderated
Related Questions
We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now.  Sin


A ladder sets against a wall at an angle α to the horizontal.  If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall ma

what is the difference between North America''s part of the total population and Africa''s part

Prime number A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers.  Examples of numbers whic

So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable

solve for k such that the system 4x+ky=6 kx+y=-3

Integrals Involving Trig Functions - Integration techniques In this part we are going to come across at quite a few integrals that are including trig functions and few metho

HOW DO WE CAN SOLVE SIMPLIFY?

Partitioning - an action of taking away or removing some objects, and finding out how many remain. (e.g., there were 15 toffees in this container, and 10 have been eaten. How many