1. Name Of Outher/Investigator: Kaustubh Chandra Joshi, (Lecturer - Mathematics)
Name and address of institution:
Government Inter College Tharkot-Balakot
Block : Bin , Distt. : Pithoragarh , State : Uttarakhand (India)
Mobile Number : 9412375389
E mail : kaustubhachandrajoshi@gmail.com

3. fofHkUu 'kkjhfjd ,ao ekufld {kerkvksa okys
fo|kfFkZ;ksa dks leku #i ls lekosf“kr fd;k tk ldrk
gSA v/;kiu gsrq fd;s x;s fof”k’V iz;Ruksa ]
fodflr midj.kksa] fHkUu &fHkUu {kerk okys
cPpksa ds rF;ksa ls lEcfU/kr ftKklkvksa]
fopkjksa] HkzkfUr;ksa vkfn ds lek/kku ds fy,
okrkoj.k gsrq iz;kl fd;s x;s gSA
vr% ifj;kstuk dk y{; f”k{kk esa u;s ,ao
ekSfyd iz;ksxksa ij vk/kkfjr Kku dks ,dhd`r dj
'kS{kf.kd iz.kkyh fodflr djuk gSA

4. fdlh 'kakDodh O;kid lehdj.k
ax2+2hxy+by2+2gx+2fy+c=0 }kjk fu#firgksrh gSA tgkW
a, h, b, g, f, c fLFkjkadgS. ifjPNsnhry ] 'kadq ds yEcorv{k ds
lkFkβ dksa.k cukrkgSA ;fn js[kk m dks js[kk l ds ifjr%bl
izdkj ?kqekrsgSa fd lHkhfLFkfr;ksa esa α vpj jgs rc mRiUu
i`"B ,dyEco`Ùkh;[kks[kykf}”kadqizkIrgksrk gSA

5. ry
α
β
f}”kadq
tud

6. tc ry ]”kadq ds ukis(“kh’kZ ds vfrfjDr) dks dkVrk gS rFkk ifjPNsnh ry ]“kadq
ds yEcor v{k ds lkFk 900 dk dksa.kcukrk gSA vFkZkr β= 900 ]]rks “kakdo ,d o`Rr
gksrk gSA ijUrq tc ry]”kadq ds ukis dks “kh’kZ ij dkVrk gS rFkk α < β ≤ 900
]ifjPNsn ,d fcUnq gksrk gSA ;fn “kkado dh f}?kkr lehdj.k ax2+2hxy+b y2
+2gx+2fy+c= o esa a = b =1 vkSj h=o gksa ]
rc x2+ y2+2gx+2fy+c =o vFkok (x2 +2gx+g2)+(y2+2fy+f2 )= g2+f2-c
vFkok (x+g)2 +(y+f)2=(g2+f2-c)1/2 ----(1) .
;fn lEcU/k (1) dh rqyuk o`Rr dh lkekU; lehdj.k (x-h)2 +(y-k)2 =r2 lsdjus ij
Kkr gksrkgS fd o`Rr dk dsUnz = (-g, -f ) rFkk
o`Rr dh f=T;k( r ) =(g2+f2-c)1/2
vr( 'kkado dh f}?kkrlehdj.k] o`Rrdks fu#fir djrh gS ] ;fn a=b ] h=o
,ao K= {P(x,y):d(P,C) = a }

7. ry
α
β
α < β ≤ 900

8. P (x, y)
C
XX1
Y
Y1
O
X2 + y2 + 2gx + 2fy + c = 0
f=T;k
(g2+f2-c)1/2
dsUnz ( -g,-f
)
Li”kZ js[kk dh lehdj.k
XX′+YY′+g(x+x′)+f(y+y′)+c=a
2
vfHkyEc js[kk dh lehdj.k
(X-x′)/(X′+g)=(Y-y′)/(Y′+f)
'kadq ifPNsndk o`Rrh;fu#i.k
Conic Section Represent Circle

9. 'kks/kifj;kstukdk lkjbl izdkjgS fd] o`Rrh;'kadqds
ifjPNsnHkkxksalsfufeZr'kadqifjPNsnftldhO;kidlehdj.k
ax2+2hxy +by2 +2gx +2fy+c=0 gksrhgS]fuEufofHkUu
fLFkfr;ksaesao`Rrdksfu#firdjrkgSA
;fn β= 900vFkoka = b , h = 0]rks'kakdo,do`RrgksrkgSA