co-ordinate geometry

All chords of the curve 3x²-y²-2x+4y=0
which subtend a right angle at origin pass through
a)(1,2)
b)(1,-2)
c)(2,1)
d)(1,1)

2 Answers

take points

x1,mx1

and x2,-x2/m

now make both of them to lie on the given curve

also the equation of the chord is given by

(x-x1)/(y-m x1) = (x1-x2)/(m x1+x2/m)

Make the curve a 2nd degree homogenous equation by replacing 2x as 2x.1 and 4y as 4y.1

now substitute the value of 1 with values frm the eqn of the chord

(take a general line lx + my + n =0)

Now since the chords subtend a right angle

coeff of x² + coeff of y² = 0

from this you'll get a simple condition on l,m,x,y

from which u 'll get (1,-2) always satisfying the condition for all values of l and m

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