Examples (NCERT) - Straight Lines Video Lecture | Mathematics for Airmen Group X - Airforce X Y / Indian Navy SSR

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part 13 let's take some example we have
been told that we have the equation of
line 3x plus 3x minus 4y plus 10 that is
Rho you define it slow and X and
y-intercept where is it well if you can
just convert this equation in the slow
form the first case I'm taking look at
the slope so what we'll do to get the
convert the equation is no form we have
y is equal to MX plus C from so this
equation we can write as 4 y is equal to
3x plus 10 correct
now since the equation is of the form Y
is equal to MX plus C we have to make Y
independent of any value so we'll divide
by 4
everything will be by therefore this
equation we get Y is equal to 3 by 4 X
plus 10 5 now we'll compare this with
this equation here if you see with X you
have em with X you have 3 by 4 so this
is nothing but our M and C is n by C is
constant it's Easter but they have not
asked us for C so we can ignore this our
answer is to take the second one second
one it is asking us to write it in the
form of snow intercept form slope
intercept form we know is of this form X
by ay plus y by B is equal to 1 so if
you can write this equation in this form
X by ay plus L is equal to 1 we had done
with our so what let us give this 3x
minus 4y plus 10 is equal to 0 let's
first write 10 in the right hand side so
what you get is 10 this is equal to
we need minus 3x plus correct you write
10 here so this was this is 10 this
becomes minus 3x plus 4 actually if you
put these values here you get 10 is you
get 2 minus 3x plus 4y I have written
this same equation as this 4 minus 3x
plus 4y squared and we will divide
everything by 10 because we wanted to
put make R is equal to 1 so what we get
is minus 3x by 10 plus 4y by 10 is 1
this is what we get same equation we can
write in this form we'll put 3 here so
we'll get X by minus 10 by 3 plus y by
similarly will make 4 here e 10 by 4 y
we have done this because we wanted to
write this equation in this form X by y
plus y by B is equal to 1 so first we
have put 10 on the right hand side
divided by 10 so we got 10 here once we
got 10 on the right hand side the left
hand side we want to three the X with
the constant so we a divided this we
haven't put this 3 here we have put this
4 here so what we got this now if you
compare this equation with this form X
by E Plus 5 is equal to 1 you can see
that e is equal to nothing but minus 10
by 3 and V is nothing but 10 PI over 4
so we have got that answer that this
x-intercept and y-intercept are minus 10
by 3 and 10 respectively
very simple what we have done in first
case when you wanted to find the slope
we have converted this equation in the
slope form and we got the slope in the
second case when we are asked to find
exit y-intercept we have just converted
this equation then the lining the
general mind equation in the slope
intercept form and we got no sorry
in the intercept form and we got with
the intercept here we are asked to
reduce the equation this in the normal
form and the fine
values of p and obviously many wonderful
reduce this equation into normal form we
have to find the bathysphere so we know
that a normal form machine is of the
small that is X cos Omega plus y also we
know that if we have equation ax plus B
y plus Z is equal to 0 and we have
equation X cos Omega plus y sine Omega
is equal to B if what the equation are
saying then we say that what do you say
that cause of my girls are going to last
minus root a by a by dou Y square plus B
Square this we have learned sine Omega
is nothing but plus minus V by a root of
a square plus B Square and P is nothing
but plus minus C by a square plus this
is what we have done now if we compare
this equation with this 3 is here y is
here
cz you compare ax plus B y plus C with a
right here a plus B my plus C is equal
to 0 in this equation what we get is a a
is equal to MU T V is equal to 1 and C
is better - these are the colors we have
R is equal to root B is equal to minus 1
and C is equal to minus 1 now things are
pretty simple you have to find the value
of cos Omega so we'll say cos Omega is
nothing but plus minus a by root a
square plus B Square this becomes plus
minus root 3 by 3 square is 3 plus 1
square is 1 so this becomes plus
yes don't three by this becomes plus
minus root three by now cos Omega square
2 plus minus root 2 by 2 therefore Omega
is equal to 30 degrees since you're
anything this is funny or in case of cos
Omega is equal to minus root 3 by 2
Omega is equal to 180 degrees minus 30
degree is equal to 150 degree so Omega
is good to either 30 degree or 150
similarly similarly sine Omega we can
find sine Omega is going to be plus
minus B by mu e square plus Z squared
sine Omega is good trash - by a square
plus B Square this becomes plus minus 1
by root 3 plus 1 so this becomes plus
minus 1 so here also if you see Omega
turns out to be 30 degree or 150 this is
one with non-marketing this is 180 plus
30 that is student this is students
because 150 is positive so this is 210
Omega is 30 or 150 here and Omega is 30
or 210 here now P is nothing but plus
minus C by root of a square plus B
square this becomes plus minus of minus
8 by root of 3 plus 1 that becomes plus
minus a by that is plus minus 4 so we
have the value of C is plus minus 4 and
Omega will take common value common one
is 30 so Omega is equal to 30 degree and
P is equal to
- listen up Omega is equal to 30 and B
is going to plus minus 4 this is the
value of Omega n P so we can buy create
the equation equation is very simple
equation is X X cos Omega there is X cos
30 degree plus y sine 30 degree is equal
to plus minus 4 so we have the equation
in first case this plus for the second
years we have minus 4 and we'll put the
values of cos 30 is sine 30 degree
enhanced let's take this example we have
two lines a 1 X plus B 1 y plus C 1 is
going to 0 and a 2 X plus B 2 y plus C 2
is equal to 0 we have to prove that if
lines are parallel if even by a demon is
going to eat Bible and they are
perpendicular if even a 2 plus b1 b2 is
convincing so let's first find the
normal the slope of these equations
because the devotion tops we can't do
anything we know that in two lines are
parallel slopes are equal and if two per
product of two spokes is equal to minus
1 that means they are perpendicular so
that means we have to find the spots to
find slopes is convert into normal form
normal form is nothing but Y is equal to
MX plus C form so let's convert equation
1 I'm taking the first first let's
convert both equation into normal form
and then then solve the question first
vision is even X plus B 1 y plus or I
can say even Y is equal to - even X
minus or you can say Y is equal to minus
a 1 by B even X - even by this is the
equation 1 so here I got M 1 is nothing
but - even by this is the first equation
however I converted this into the normal
form and I compared this equation with
this equation I see that this is M
whatever you use for multiply with X is
M
yeah you multiplied - even by be one
with the exo-m is - even by similarly
for equation do we have a 2x + V 2 y
plus c2 is equal to zero this equation I
can write in this form Y is equal to
minus a2 by b2 x + CD by V 2 is equal to
is it good it's gonna do this so from
this we get M is equal to minus e2 by
this is my equation number 2 this is 1
and this is so we have two equations and
this M 1 is going to be able to be in
empties but we do we do I took a
shortcut because this is almost same but
the steps are almost seen now we have
put em in now let's take the case one
the case one is both the lines are
parallel in case both the lines of
Mandal we see MN is going to correct now
if you see ml squared lambda we can say
or M that is nothing but - even maybe
even and emptily is nothing but minus du
by - - can cancel or we can say that
even by V 1 is equal to 8 to 5 and that
is what we are supposed to answer so you
see you have to prove that in their
panel even might be one is worth doing
well now let us take the case - we have
both are perpendicular this was bad give
a perpendicular m1 into m2 plus 1 is
equal to 0 you know this so we'll say m1
is nothing but - even by even into minus
a2 by b2 plus 1 is correct we have this
minus into minus plus so what we get is
a1 a2 + by V 1 V 2 V will be 2 + 1
is equal to or the same equation again
is even 8 plus V 1 V 2 by V 1 V 2 Oh
the same equation again by there's even
a 2 plus V 1 V 2 variables and that is
what we are supposed to even into plus V
1 V 2 is very very simple
the approach we followed that we were
asked to prove that this lines are
parallel and perpendicular if this nice
apparent but really this equation should
so we were asked to prove that in this
lines are parallel or perpendicular
particular equations are satisfied thus
we knew that somewhere we have to find a
slope because we know that if the lines
are parallel we use em - but if the
lines of a pedal here we say m1 into m2
plus 130 so for both the equation the
general equation of the line we had even
Express beam and microsiemens go to 0
and into X plus C 2 V 2 y plus C 2 equal
to 0 we found the stones we found M that
is equal to minus given by B 1 and M 2
is going to - a 2-byte and thus we have
used this equation M is equal to M to
get even will be when is equal to e 2 by
B 2 and M into M 2 plus 1 is equal to 0
we got even a 2 plus B 1 B this will do
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