CBSE Class 11-science Answered

Find the co-ordiantes of the foci, the vertices, the length of major axis, the minor axis the eccentricity and the length of the latus rectum of the ellipse.

Asked by Topperlearning User | 13 Nov, 2016, 08:09: PM

Expert Answer

$a right parenthesis x squared over 36 plus y squared over 16 equals 1 A x i s space i s space X minus a x i s a equals 6 space comma space b equals 4 space e equals square root of 1 minus b squared over a squared end root equals square root of 1 minus 16 over 36 end root equals fraction numerator square root of 20 over denominator 6 end fraction F o c i i equals left parenthesis plus-or-minus a e comma 0 right parenthesis equals left parenthesis plus-or-minus square root of 20 comma 0 right parenthesis V e r t i c e s equals left parenthesis plus-or-minus a comma 0 right parenthesis equals left parenthesis plus-or-minus 6 comma 0 right parenthesis L e n g t h space o f space m a j o r space a x i s equals 2 a equals 12 L e n g t h space o f space m i n o r space a x i s equals 2 b equals 8 L e n g t h space o f space l a t u s space r e c t u m equals fraction numerator 2 b squared over denominator a end fraction equals fraction numerator 2.16 over denominator 6 end fraction equals 16 over 3 b right parenthesis x squared over 16 plus y squared over 36 equals 1 A x i s space i s space Y minus a x i s a equals 4 space comma space b equals 6 space e equals square root of 1 minus a squared over b squared end root equals square root of 1 minus 16 over 36 end root equals fraction numerator square root of 20 over denominator 6 end fraction F o c i i equals left parenthesis 0 comma plus-or-minus b e right parenthesis equals left parenthesis 0 comma plus-or-minus square root of 20 right parenthesis V e r t i c e s equals left parenthesis 0 comma plus-or-minus b right parenthesis equals left parenthesis 0 comma plus-or-minus 6 right parenthesis L e n g t h space o f space m a j o r space a x i s equals 2 b equals 12 L e n g t h space o f space m i n o r space a x i s equals 2 a equals 8 L e n g t h space o f space l a t u s space r e c t u m equals fraction numerator 2 a squared over denominator b end fraction equals fraction numerator 2.16 over denominator 6 end fraction equals 16 over 3 c right parenthesis 36 x squared plus 4 y squared equals 144 rightwards double arrow x squared over 4 plus y squared over 36 equals 1 A x i s space i s space Y minus a x i s a equals 2 comma space b equals 6 space e equals square root of 1 minus a squared over b squared end root equals square root of 1 minus 4 over 36 end root equals fraction numerator square root of 32 over denominator 6 end fraction F o c i i equals left parenthesis 0 comma plus-or-minus b e right parenthesis equals left parenthesis 0 comma plus-or-minus square root of 32 right parenthesis V e r t i c e s equals left parenthesis 0 comma plus-or-minus b right parenthesis equals left parenthesis 0 comma plus-or-minus 6 right parenthesis L e n g t h space o f space m a j o r space a x i s equals 2 b equals 12 L e n g t h space o f space m i n o r space a x i s equals 2 a equals 4 L e n g t h space o f space l a t u s space r e c t u m equals fraction numerator 2 a squared over denominator b end fraction equals fraction numerator 2.4 over denominator 6 end fraction equals 4 over 3 d right parenthesis 4 x squared plus 9 y squared equals 36 rightwards double arrow x squared over 9 plus y squared over 4 equals 1 A x i s space i s space X minus a x i s a equals 3 space comma space b equals 2 space e equals square root of 1 minus b squared over a squared end root equals square root of 1 minus 4 over 9 end root equals fraction numerator square root of 5 over denominator 3 end fraction F o c i i equals left parenthesis plus-or-minus a e comma 0 right parenthesis equals left parenthesis plus-or-minus square root of 5 comma 0 right parenthesis V e r t i c e s equals left parenthesis plus-or-minus a comma 0 right parenthesis equals left parenthesis plus-or-minus 3 comma 0 right parenthesis L e n g t h space o f space m a j o r space a x i s equals 2 a equals 6 L e n g t h space o f space m i n o r space a x i s equals 2 b equals 4 L e n g t h space o f space l a t u s space r e c t u m equals fraction numerator 2 b squared over denominator a end fraction equals fraction numerator 2.4 over denominator 3 end fraction equals 8 over 3$