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Please solve how to find k=0,2,1/3

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Asked by sanjaysingh.srct 19th September 2019, 12:36 PM
Answered by Expert
Answer:
Line x-2y+3=0 meet the axes at points A(0,3/2) and B(-3,0)
Line y=kx-1 meet the y axis at point C(0,-1)
Since the above two lines meet the axes in concyclic points
So, the above 3 points satisfies the equation of a circle given by
x squared plus y squared plus 2 g x plus 2 f y plus c equals 0
rightwards double arrow 9 over 4 plus 3 f plus c equals 0 space... space left parenthesis i right parenthesis comma space
6 g equals 9 plus c space.... space left parenthesis i i right parenthesis space a n d
1 minus 2 f plus c equals 0 space... space left parenthesis i i i right parenthesis
S o l v i n g space left parenthesis i right parenthesis comma space left parenthesis i i right parenthesis space a n d space left parenthesis i i i right parenthesis space s i m u l tan e o u s l y comma space w e space h a v e
f equals negative 1 fourth comma space g equals 5 over 4 space a n d space c equals negative 3 over 2
E q space o f space c i r c l e space b e c o m e s space
2 x squared plus 2 y squared plus 5 x minus y minus 3 equals 0
T h i s space c i r c l e space c u t s space t h e space x minus a x i s space a t space t h e space p o i n t s space w h e r e space y equals 0
T a k e space y equals 0
rightwards double arrow 2 x squared plus 5 x minus 3 equals 0
rightwards double arrow x equals negative 3 space O R space x equals 1 half
T h e r e f o r e comma space t h e space c i r c l e space c u t s space t h e space x minus a x i s space a t space t h e space p o i n t space D open parentheses 1 half comma 0 close parentheses space o t h e r space A comma B comma C
T h e space l i n e space y equals k x minus 1 space c u t s space t h e space y minus a x i s space a t space C
T h e r e f o r e comma space t h e space a b o v e space l i n e space c u t s space t h e space x minus a x i s space a t space D open parentheses 1 half comma 0 close parentheses
N o w comma space t h e space e q space o f space l i n e space p a s sin g space t h r o u g h space C space a n d space D space i s
y equals 2 x minus 1
H e n c e comma space k equals 2
Answered by Expert 20th September 2019, 11:20 AM
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