Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

The line mx-y-m-2=0 meets the circle x^2+y^2-4x+6y-3=0 at A and B.The lines joining A and B to the centre meet the circle again at C and D.If m is the parameter and set of lines CD are concurrent at p(a,b) then the value of a-b equals.
Asked by Sunil Soni | 23 Sep, 2015, 10:29: AM
answered-by-expert Expert Answer
 
T h e space e q u a t i o n space o f space t h e space c i r c l e space i n space s tan d a r d space f o r m space i s open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 squared. T h e space c o o r d i n a t e s space o f space t h e space c e n t e r space a r e space left parenthesis 2 comma space minus 3 right parenthesis T h e space e n d s space o f space t h e space c h o r d space A B space a n d space t h e space c e n t e r space o f space t h e space c i r c l e space a r e space j o i n e d space t o space g e t space C space a n d space D space r e s p e c t i v e l y. space H e n c e comma space A c space a n d space B D space a r e space t h e space d i a m e t e r s. A l s o. space t h e space t r i a n g l e s space A O B space a n d space C O D space a r e space c o n g r u e n t. H e n c e comma space A B vertical line vertical line C D. E q u a t i o n space o f space A B space i s space y equals m x minus m minus 2 L e t space t h e space e q u a t i o n space o f space C D space b e space y equals m x plus K S i n c e comma space i t space p a s s e s space t h r o u g h space left parenthesis a comma space b right parenthesis comma space w e space g e t b equals m a plus K rightwards double arrow K equals b minus m a H e n c e comma space e q u a t i o n space o f space C D space i s space y equals m x plus b minus m a. H e r e space apostrophe m apostrophe space i s space a space p a r a m e t e r space w h i c h space c a n space t a k e space d i f f e r e n t space v a l u e s. F o r space m equals 1 comma space e q u a t i o n space o f space C D space i s space y equals x plus b minus a E q u a t i o n space o f space A B space i s space y equals x minus 3 D i s tan c e space o f space y equals x minus 3 space f r o m space left parenthesis 2 comma space minus 3 right parenthesis space i s space open vertical bar fraction numerator 2 minus open parentheses negative 3 close parentheses minus 3 over denominator square root of 1 squared plus 1 squared end root end fraction close vertical bar equals fraction numerator 2 over denominator square root of 2 end fraction D i s tan c e space o f space C D space f r o m space left parenthesis 2 comma space minus 3 right parenthesis space i s open vertical bar fraction numerator 2 minus open parentheses negative 3 close parentheses plus b minus a over denominator square root of 1 squared plus 1 squared end root end fraction close vertical bar equals fraction numerator 1 over denominator square root of 2 end fraction open vertical bar 5 plus b minus a close vertical bar B o t h space t h e space d i a tan c e s space a r e space e q u a l. H e n c e comma space fraction numerator 2 over denominator square root of 2 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction open vertical bar 5 plus b minus a close vertical bar rightwards double arrow open vertical bar 5 plus b minus a close vertical bar equals 2 rightwards double arrow b minus a equals negative 5 plus-or-minus 2 rightwards double arrow b minus a equals negative 7 space left parenthesis r e j e c t i n g space b minus a equals negative 3 space sin c e space i t space g i v e s space t h e space e q u a t i o n space o f space A B right parenthesis H e n c e comma space a minus b equals 7
Answered by satyajit samal | 24 Sep, 2015, 12:04: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 11-science - Maths
2 one
question image
Asked by dra | 24 Feb, 2024, 06:35: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
find the coordinates of the centre of a circle passing through the points(0,0),(-2,1)and(-3,2).also , find its radius .
question image
Asked by shakyajayprakash2006 | 08 Jun, 2022, 05:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Examine whether the point (4, 5) lies outside or inside the circle of equation x^2+y^2-2x-3=0
Asked by sbipo2000 | 23 Feb, 2020, 03:43: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
SIR PLEASE HELP ME WITH THIS QUESTIONS : 1. Find the equation of the tangent to the circle x^2+y^2=16 drawn from the point (1,4). 2. How many triangles can be formed by joining any 3 of the 9 points when i) no 3 of them  are collinear? ii) 5 of them are collinear? 3. AB is a line of fixed length, 6 units, joining the points A(t,0) and B which lies on thepositive y axis. P is a point on AB distant 2 units from A. Express the coordinates of B and P in terms of t. Find the locus of P as t varies. 4. In a triangle ABC, (b^2 - c^2) / (b^2 + c^2) = sin(B - C) / sin(B + C), prove that it is either a right-angled or isoceles triangle.
Asked by kandappan | 08 Feb, 2020, 11:29: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
6
question image
Asked by gauravmore604 | 04 Nov, 2019, 03:31: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
The locus of point for which sum of the squares of distances from cordinate axes is 25 is
Asked by Tejravi969 | 19 Aug, 2019, 06:08: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)  
Asked by rushabh1234 | 23 Jan, 2019, 08:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the circle with centre (-2,3) and radius 4.
Asked by Topperlearning User | 30 Apr, 2014, 11:08: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the centre and radius of the circle given by the equation (x + 5)2 + (y + 1 )2 = 9
Asked by Topperlearning User | 25 Apr, 2014, 09:39: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the co-ordinates of the centre and the radius of the circle given by the equation x2 + y2 + 6x - 8y - 24 = 0.
Asked by Topperlearning User | 25 Apr, 2014, 09:11: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×