General Equation of Straight lines (Part - 13) - Straight line, Mathematics, Class 11 Video Lecture - Class 11 | Best Video for Class 11

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part 13 is brought to you by exam fear
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watching this video please make sure
that you have a straight line part 1 -
Bart bellman now we'll study general
equation of straight lines general
equation of straight lines is denoted by
a x + B y plus C is equal to 0 please no
ax plus B y plus C is equal to 0 where a
B and C are real constants such that a
and we are not to be the zero
simultaneously because if both a and B
are 0 this is the C is equal to 0 that
doesn't that is not a straight line
equation straight line equation should
have either one X component or one by
component or would X in my company that
that's why both a and we can't be 0
Cerritos be general equation of a line
is ax plus B y plus C is equal to 0
where what a and we can't be 0 some
endlessly as easy a 0 or B 0 or both are
not 0 but what a and we can't be 0
simultaneously example 3x plus 4y plus 3
is equal to 0 this is my equation of the
straight line if you say 3x plus 3 is
equal to 0 that is also equation no
straight line because here B is equal to
0 is not equal to 0 if you say 4y plus 5
is equal to 0 this is the equation of
straight line here you see a 0 here be
easy but if you say put a mean 0 if we
just say Phi dependence 0 this is not
the equation of straight line or you say
0 0 0 this is not an equation of
straight line or line to be creation of
straight line it should have at least X
component or Y component or both x and y
now there are different forms of X plus
B by plus C they are slope intercept
form intercept form
and normal form these are the three
forms of ax plus B y plus C is equal to
0 I will show you let's discuss
slope-intercept form so in this case we
have this equation ax plus B y plus C is
below 0 and then B is not equal to 0
because we are dividing the work
equation by B if B is equal to 0 this
means right so if E is not equal to 0
this equation can be written as in this
form if you divide for example we have a
X plus 0 if you divide by B the
valuation by B this becomes 0 by D so
what you get is a by B of X plus y plus
C by B is producer or we can write this
equation in this form Y is equal to
minus a by B X minus C by so if you see
this equation and if I say Y is equal to
MX plus C both are of similar pattern
the pattern is same that's why we can
say m is nothing but minus B by B and C
is nothing but minus C by correct that
is what we have proved in a rather so
same equation X plus B by plus C we have
written in the comma slope intercept
form here please know that B is not
equal to 0 thus we have seen that we
have written this equation ax plus B by
plus C in this form slope intercept form
in slope intercept form we know the
slope and we know the intercept so we
have written this equation in slope
intercept No
next is intercept form intercept form as
we know is nothing but X by ay plus y by
B is equal to 1 where is the intercept
in x-axis V is the anus
my ex's so it's me the same equation e
explode you've ever seen you can write
in this form
I'll show you how so this equation we
have a X plus vdy plus C correct let us
divide the whole equation by C so what
we get is K by CX plus V by C 1 is equal
to minus 1 or if you put 1 this side
because we have to find it is equal to 1
in this form so this becomes minus a by
C X minus or plus minus of V by C by is
equal to 1 correct
now what we can do is we can divide this
equation by you simply we arrive in this
form X by minus C Y we can write this we
have just put a little X plus y by minus
B by C so rig minus C by V is equal to 1
so C in equation we have written in this
form that is X by minus C by e plus y by
minus C by B is equal to 1 and this
equation is if you see similar to this
equation is equal to 1 is y plus 1 is
equal to 1 here we see that a is minus C
by and E is minus sin Phi thus what we
have seen is we have written this form
of equation as general form of equation
in the intercept form in such case the a
becomes minus C by a and B becomes minus
C by E now let's say normal form
normal form we know is of this form X
cos Omega plus y sine Omega is going to
be so we can rewrite this equation ax
plus B y plus C is equal to 0 in this
one I'll show you how so let me write
this equation ax plus
be y plus C is equal to zero as we can
write this equation as ax plus B y is
equal to minus C correct this is our
equation 1 also the equation 2 we have
as this one X cos Omega L right cos
Omega into X plus sine Omega into y is
equal to so if we can see these two
equations we can compare same form the
pattern is almost same so we can say
that we divide this equation 1 by
equation 2 what we get is a by cos Omega
is equal to B by sine Omega is you can
do minus C by P correct because this
fish is almost same the X Y and constant
the same fashions we can write like this
all from this what we get is cos Omega
is equal to cos Omega s but do a B by C
minus V by this is the value of cos
Omega and sine Omega will be minus B P
by C minus V B banks so we have God this
is 3 and this is should we have got sine
Omega and gospel now we know that sine
square plus cos square is not the one we
know so I'm going to square these two so
we know that sine square Omega plus cos
square Omega spur to 1 we know this or
minus a B by C whole square plus minus B
by C whole square this is equal to 1 or
what I get is a square e square C square
speed
plus b square e square C square this
balloon or a square plus B Square will
take in here I get v square by C square
is equal to 1 correct
a square plus B square at the common or
I can write B is equal to nothing but C
by of a square plus B correct
because P Square will be C square by a
square plus B Square so P will be C by a
root a square plus B square so this is
the equation fine so we have found the
value of cos Omega sine Omega and B so
if you see cos Omega is plus minus sorry
this will become equal to plus minus C
that is now we have value of T in cos
Omega we have NC also will replace the
value of P with this C by root a square
with a spine so we get cos Omega is
gonna do minus a by C into P but this C
into Lu a square plus B Square and since
plus minus was there so that's minus
here so this becomes CC cancel so this
becomes a by root a square plus plus
similarly for sine Omega we have minus V
by C so this becomes minus V by C into C
by mu a square plus B Square minus plus
so this becomes CC cancel this becomes V
by nu e square plus and that is what we
have written here you see cos Omega is
equal to plus minus a by root a square
plus B square sine Omega is equal to
plus minus V by root a square plus B
Square and P is equal to plus minus root
a square plus please
does we see that we have written this
equation ax plus B y plus C that is a
general equation of line in the normal
form in the normal form we know the
length of the normal and the angle which
the normal makes with the positive
x-axis for example this is the XY axis
this is a line this is a normal and if
you draw this moment from Perez in this
is the angle Omega and this is P and
this is the half-life for this equation
for this form of line we have this
equation x cos omega was y sine Omega is
equal to P so thus we have seen that we
can write the general form of equation
in slope form slope-intercept form where
we have one slope and one intercept
intercept form where we have gained even
with intercept and normal form where we
have normal and anglerfish normal makes
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