Dear students todays topic is circle.
This
is again a very important topic. First you
have to remember all forms of an equation of a circle.
Here tangency part is very important. To get equation of a tangent to circle (actually to any curve) at a point (x1,y1) on it we have to replace x2 by xx1 y2 by yy1 2x by x + x1 2y by y + y1 and Keep constant term unchanged !
Generally we consider four parts in tangency:
1) To obtain equation of a tangent to circle at a point (x1, y1) on it.
2) To find the condition that line y = mx + c is tangent to circle
3) To show that in general two tangents can be drawn to circle from a point (x1, y1) in the same plane. For this we obtain a Q.E. in slope m.
4) To find locus of points tangents from which to the circle are at right angles.
Note that (2), (3), (4) are obtained for standard circle only.
e.g. to get
director circle of x2 + y2+ 2gx + 2fy + c = 0, you
cannot
use x2 + y2 = 2a2. Here you have to use the
fact that for director circle (locus of points tangents from which to the given
circle are at right angles) centre is the same and radius is 
times the radius of
given circle. You have to remember equation of for circle x2 + y2 + 2gx + 2fy + c = 0
i) length of
intercept on X axis is 
and on Y axis it is 
ii) If g2 = f2 = C then circle touches both axes.
If
you are asked point of contact of tangent to a circle, just check the options
as that point lies on both! Length of tangent segment to a circle is 
. The concept of
touching circles is important. For two distinct circles number of common
tangents is
1) O, if circles are concentric.
2) 1, if circles touch each other internally
3) 2, if circles intersect at two points.
4) 3, if circles touch each other externally
5) 4, if d(C1 C2) > r1 + r2 i.e. circles neither intersect nor touch each other. In case of circle, in many cases first check options for correct answer.
Happy eLearning!
-Team Ednexa
www.ednexa.com
5 Comments
thankd
thanks
thanks
sir will u tell me about the admission process for autonomous colleges????
sir will u tell me about the admission process for autonomous colleges????
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