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Analytical Geometry

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15 Oct 2009 20:08:42 IST

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Q 1 :Find the locus of the middle points of the intercepts made by the axes on the lines drawn t

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Q 1 :Find the locus of the middle points of the intercepts made by the axes on the lines drawn thru the pt(a,b)

Q2 : A line forms a ∆ of area 54√3 sq unts wid d coordinate axis.find the eqn of the line if the perpendicular drawn frm the origin makes an angle of 60 wid the + x axisQ3 :In a ∆ABC d(20,25) & e(8,16) are the foot of perpendicular frm A & B to the opp. sides . if c(10,15) find the orthocentre.

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Comments (5)

Bipin Dubey

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15 Oct 2009 20:15:44 IST

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Let the line intersects axes at (p,0) and (0,q)

equation of line : x/p + y/q = 1

since (a,b) passes through the line : a/p + b/q = 1

mid point of (p,0) and (0,q) is (p/2,q/2) = (h,k) let => p-2h, q=2k

so, a/2h + b/2k = 1

locus of (h,k) is a/x + b/y = 2 => ay+bx = 2xy

Nikhil Gupta

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15 Oct 2009 22:49:01 IST

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Sol 2---

Let the length of perpendicular drawn from the origin to the line be p...

Then a = p/cos60

b = p/sin60 (where a and b are x- and y- axis intercepts respectively)

Now

Ar(triangle) = 54√3 = 1/2 *base*height = 1/2 * (p/sin60)*(p/cos60)

=> p = 9

=> a= 18/√3 and b= 18

Hence eqn of line is x/18√3 + y/ 18 = 1

Tell me if i'm right or not

vibhor gupta

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15 Oct 2009 23:24:22 IST

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no nikhhil i m nt satisfied

kabi

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16 Oct 2009 00:23:09 IST

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hello

we have D ( 20,25) E ( 8,16) C( 10,15 )

slope of AC = -1/2

slope of BC = 1

Thus slope of BE = 2 and that of AD = -1

thus the eq. of AD becomes y +x = 45

eq. of BE is y = 2x

the point of concurrency is x = 15 y=30 ie. coordinate of orthocenter .

thank u sorry if there is a calculation mistake as i m solving in hurry .

one more thing the approach used by the student who have given the second answer is correct .

ankur gupta

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23 Oct 2009 22:19:20 IST

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2) i m just correcting nikhil's sol....

nikhil method is correct till p=9

now , a = p/cos60 = 18and b= p/sin60 = 18/sqrt(3)

so, the equation of line is

x/18 + ysqrt(3)/18 =1

x + ysqrt(3) = 18

hope u gt it .....in case of ny problem tl me...

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