IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

BALGANESH

1] A straight line through A(-2, -3) cut the lines x + 3y = 9

and x + y + 1 = 0 at B and C respectively. Find the equation

of the line if AB x AC = 20

2] In the angle ABC, the equations of AB and AC are 2x + 3y = 29

and x + 2y = 16. If the median through A cuts BC at (5, 6) find the

equation of the side BC.

sboosy

consider the eqn of line to b

x+2/cosa =y+3/sina=r

x=rcosa-2

y=rsina-3

for r=r1 the pt lies on the 1st given line

so rcosa+3rsina+20

r=r2 it lies on second line

so rcosa+rsina=4

r1*r2=20

so 80/(3sina+cosa)(cosa+sina)=20

solving 2sin2a-cos2a=2

it satisfies for a=pi/4

hence the answer

sboosy

Let the point B on AB b (h1,k1)
Let the point C on AC b (h2,k2)

we form 2 equations respectively bcos they lie on the given lines

not only that since midpt is 5,6
h1+h2=10
k1+k2=12

2 equations 2 unknowns

hence the answer

raulrag009

q2
hey man

it's simple

let pt of int of AB,BC and BC,AC be x1,y1and x2,y2 respectively
since 5,6 is the mid point of bc

therefore x1+x2=10 and y1+y2=12.

since x1,y1 lies on 2x+3y=29
it will satisfy 2x1+3y1=29

similarly x2+2y2=16

u got 4 eqn's

u will get values as x1,y1=4,7
and x2,y2=6,5

now u can find slope and then find eqn of BC easily

ans should be x+y=11.

rate if useful

nudge if not satisfied

ayshwarya

hey guys let d eqn b mx-y+2m-3=0 hence by solvng dis eqn wid d oder 2 u wud get B & C hence as per gven data dat AB X AC =20 find m & substitute m in it itsidea wich comes in our minds try dis

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