ELLIPSE. 1. If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is [Karnataka CET 2000]

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1 ELLIPSE. If the ltus rectum of ellipse e equl to hlf of its mior is, the its eccetricit is [Krtk CET 000] / / / d /. The legth of the ltus rectum of the ellipse is [MNR 7, 0, ] / / / d 0/. Eccetricit of the coic 6 7 is [MNR ] / 7 7/6 / d /. The legths of mjor d mior is of ellipse re 0 d respectivel d its mjor is log the -is. The equtio of the ellipse referred to its cetre s origi is [P. CET 00] 6 6 d If the cetre, oe of the foci d semi-mjor is of ellipse e 0, 0, 0, d the its equtio is [AMU ] The equtio 0 represets [MP PET ] A circle A ellipse A hperol d A prol 7. The equtio of the ellipse whose ltus rectum is d whose eccetricit is, referred to the pricipl es of coordites, is [MP PET ] d 6 6. For the ellipse, the legth of ltus rectum is [MNR 7] d. For the ellipse, the eccetricit is [MNR 7] 6 7 d

2 0. If the legth of the mjor is of ellipse is three times the legth of its mior is, the its eccetricit is [EAMCET 0] d. The legth of the ltus rectum of ellipse is of the mjor is. Its eccetricit is 7 d [EAMCET ]. A ellipse is descried usig edless strig which is pssed over two pis. If the es re 6 cm d cm, the ecessr legth of the strig d the distce etwee the pis respectivel i cm, re [MNR ] 6, 6,, r r. The equtio 0 represets ellipse, if [MP PET ] r r r. The locus of the poit of itersectio of perpediculr tgets to the ellipse, is d [MP PET ]. The legth of the ltus rectum of the ellipse [Krtk CET ] 6 /6 7/7 7/ d / 6. The equtio of the ellipse whose oe focus is t, 0 d whose eccetricit is /, is [Krtk CET ] d 7. The foci of 6 00 re [BIT Rchi 6], 0 0,, d,. Eccetricit of the ellipse is [Kerl Egg. 00] d

3 . The legth of the ltus rectum of the ellipse, is [MP PET ] d 0. The locus of vrile poit whose distce from, 0 is times its distce from the lie, is [IIT ] Ellipse Prol Hperol. If P,,, 0 F, 0 d 6 00, the PF PF equls [IIT ] 6 0 d. P is poit o the ellipse 6, whose foci re S d S. The SP S' P equls [DCE ] 6 d. Wht is the equtio of the ellipse with foci, 0 d eccetricit 0 d 0 [DCE ]. The eccetricit of the ellipse 6, is [MP PET 000] d 6. The eccetricit of the ellipse 6 00 is [MP PET 00] / / / d / 6. The distce etwee the foci of ellipse is 6 d eccetricit is. Legth of the mjor is of the ellipse is [Krtk CET 00] 6 6 d 7. If the eccetricit of the two ellipse d re equl, the the vlue of 6 is [UPSEAT 00] / 6/ / d /6. I the ellipse, mior is is d eccetricit is. The mjor is is [Krtk CET 00] 6 0 d 6. I ellipse, the distce etwee the foci is [Krtk CET 00] /

4 d 0. Equtio of the ellipse with eccetricit d foci t, 0 is [MP PET 00]. The sum of focl distces of poit o the ellipse with mjor d mior es s d respectivel, is equl to [MP PET 00] d. I ellipse the distce etwee its foci is 6 d its mior is is. The its eccetricit is [EAMCET ] d. If r of give legth moves with its etremities o two fied stright lies t right gles, the the locus of poit o r mrked o the r descries / [Oriss JEE 00] Circle Prol Ellipse d Hperol. The cetre of the ellipse is [MP PET ],,, d,. Ltus rectum of ellipse 6 0 is [MP PET ] / / d 6/ 6. The equtio 7 0 represets [BIT Rchi 6] A circle A ellipse A hperol d A rectgulr hperol 6 7. The cetre of the ellipse is [EAMCET ] 0, 0,, 0 d 0,. The equtio of ellipse whose focus,, whose directri is 0 d whose eccetricit is, is give [MP PET ] d The foci of the ellipse re t [MNR ; MP PET ;], d, 6, d 6,

5 , d, 6 d, d, 6 0. The eccetricit of the ellipse 0 0, is [MNR ; P. CET 00] / / /. The curve represeted cos t sit, cos t sit is [EAMCET ; DCE 000] Ellipse Prol Hperol d Circle. The eccetricit of the ellipse 6 0 is [MP PET 6] 6 d. The eccetricit of the curve represeted the equtio 0 is [Roorkee ] 0 / / d. For the ellipse the eccetricit e [Krtk CET 00] / / / d /. The eccetricit of the ellipse is [AMU ] / / / d Imgir 6. The legth of the es of the coic 6 0, re [Oriss JEE 00],,, d, 7. The eccetricit of the ellipse 6 0 is [EAMCET 00] / / / d /. The eccetricit of the coic 6 is [MP PET 00] d. If the lie c e tget to the ellipse 6 d, the c [MNR 7; DCE 000] 0. The positio of the poit, with respect to the ellipse [MP PET ] Outside the ellipse O the ellipse O the mjor is d O the mior is

6 . The gle etwee the pir of tgets drw to the ellipse from the poit,, is [MNR ] t t 6 t d t. The equtios of the tgets of the ellipse 6 which psses through the poit, is [MP PET 6],,, d,. If the lie m c touches the ellipse m m m d m. The ellipse d the stright lie m c m c m c d c, the c [MNR 7; MP PET ] m c itersect i rel poits ol if [MNR ]. The locus of the poit of itersectio of the perpediculr tgets to the ellipse is d [Krtk CET 00] 6. Eccetric gle of poit o the ellipse 6 t distce uits from the cetre of the ellipse is [WB JEE 0] d, 7. The equtio of the tgets drw t the eds of the mjor is of the ellipse 0 0 re [MP PET ] 0, 6. The equtio of orml t the poit 0, of the ellipse is [MP PET ] 0 0 -is d -is. The equtio of the orml t the poit, o the ellipse 6 0, is [MP PET 000] d If the lie cos si p e orml to the ellipse, the [MP PET 00] p cos si p cos si p sec cosec

7 d cosec sec p 6. The lie 0 m l is orml to the ellipse, if [DCE 000] l m m l m l

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