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Asked by araima2001 | 28th Feb, 2017, 11:47: AM

Expert Answer:

begin mathsize 16px style straight L colon space ax squared plus 3 xy minus 2 straight y squared minus 7 straight x plus straight y plus straight c equals 0
Comparing space with space the space standard space equation comma
ax squared plus 2 hxy plus by squared plus 2 gx plus 2 fy plus straight c equals 0 comma space we space get
straight a comma space straight b comma space straight c comma space straight h equals 3 over 2 comma space straight b equals negative 2 comma space straight g equals fraction numerator negative 7 over denominator 2 end fraction comma space straight f equals 1 half
We space know space that comma space for space straight a space pair space of space straight space lines comma space the space angle comma space straight Q comma space which space is space between space them space
is space given space by comma space straight Q equals tan to the power of negative 1 end exponent open square brackets fraction numerator 2 square root of straight h squared minus ab end root over denominator straight a plus straight b end fraction close square brackets
As space per space the space question comma space straight Q equals straight pi over 2 space for space which space straight a space plus space straight b equals 0 rightwards double arrow straight a equals 2
Also comma space it space is space pertinent space to space note space here space that space such space straight a space representation space left parenthesis of space pair space of space lines right parenthesis
is space possible space only space if comma
open vertical bar table row straight a straight h straight g row straight h straight b straight f row straight g straight f straight c end table close vertical bar equals 0
Substituting space the space values space for space open vertical bar table row straight a straight h straight g row straight h straight b straight f row straight g straight f straight c end table close vertical bar equals 0 rightwards double arrow open vertical bar table row 2 cell 3 over 2 end cell cell fraction numerator negative 7 over denominator 2 end fraction end cell row cell 3 over 2 end cell cell negative 2 end cell cell 1 half end cell row cell fraction numerator negative 7 over denominator 2 end fraction end cell cell 1 half end cell straight c end table close vertical bar equals 0
rightwards double arrow 2 open parentheses negative 2 straight c minus 1 fourth close parentheses minus 3 over 2 open parentheses fraction numerator 3 straight c over denominator 2 end fraction plus 7 over 4 close parentheses minus 7 over 2 open parentheses 3 over 4 minus 7 close parentheses equals 0
rightwards double arrow negative 4 straight c minus 1 half minus fraction numerator 9 straight c over denominator 4 end fraction minus 21 over 8 minus 21 over 8 plus 49 over 8 equals 0
rightwards double arrow negative fraction numerator 25 straight c over denominator 4 end fraction minus 21 over 4 plus 24 equals 0
rightwards double arrow negative 25 straight c minus 21 plus 96 equals 0
rightwards double arrow negative 25 straight c plus 75 equals 0
rightwards double arrow straight c equals 3
Hence comma space the space complete space equation space is space straight L colon space 2 straight x squared plus 3 xy minus 2 straight y squared minus 7 straight x plus straight y plus 3 equals 0
Now comma space 2 straight x squared plus 3 xy minus 2 straight y squared
equals 2 straight x squared plus 4 xy minus xy minus 2 straight y squared
equals 2 straight x left parenthesis straight x plus 2 straight y right parenthesis minus straight y left parenthesis 2 straight y plus straight x right parenthesis
straight L colon space ax squared plus 3 xy minus 2 straight y squared minus 7 straight x plus straight y plus straight c equals 0
Comparing space with space the space standard space equation comma
ax squared plus 2 hxy plus by squared plus 2 gx plus 2 fy plus straight c equals 0 comma space we space get
straight a comma space straight b comma space straight c comma space straight h equals 3 over 2 comma space straight b equals negative 2 comma space straight g equals fraction numerator negative 7 over denominator 2 end fraction comma space straight f equals 1 half
We space know space that comma space for space straight a space pair space of space straight space lines comma space the space angle comma space straight Q comma space which space is space between space them space
is space given space by comma space straight Q equals tan to the power of negative 1 end exponent open square brackets fraction numerator 2 square root of straight h squared minus ab end root over denominator straight a plus straight b end fraction close square brackets
As space per space the space question comma space straight Q equals straight pi over 2 space for space which space straight a space plus space straight b equals 0 rightwards double arrow straight a equals 2
Also comma space it space is space pertinent space to space note space here space that space such space straight a space representation space left parenthesis of space pair space of space lines right parenthesis
is space possible space only space if comma
open vertical bar table row straight a straight h straight g row straight h straight b straight f row straight g straight f straight c end table close vertical bar equals 0
Substituting space the space values space for space open vertical bar table row straight a straight h straight g row straight h straight b straight f row straight g straight f straight c end table close vertical bar equals 0 rightwards double arrow open vertical bar table row 2 cell 3 over 2 end cell cell fraction numerator negative 7 over denominator 2 end fraction end cell row cell 3 over 2 end cell cell negative 2 end cell cell 1 half end cell row cell fraction numerator negative 7 over denominator 2 end fraction end cell cell 1 half end cell straight c end table close vertical bar equals 0
rightwards double arrow 2 open parentheses negative 2 straight c minus 1 fourth close parentheses minus 3 over 2 open parentheses fraction numerator 3 straight c over denominator 2 end fraction plus 7 over 4 close parentheses minus 7 over 2 open parentheses 3 over 4 minus 7 close parentheses equals 0
rightwards double arrow negative 4 straight c minus 1 half minus fraction numerator 9 straight c over denominator 4 end fraction minus 21 over 8 minus 21 over 8 plus 49 over 8 equals 0
rightwards double arrow negative fraction numerator 25 straight c over denominator 4 end fraction minus 21 over 4 plus 24 equals 0
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Answered by Rebecca Fernandes | 28th Feb, 2017, 01:28: PM