Question

the locus of the middle points of the chords of hyperbola 3x^2-2y^2+4x-6y=0 parallel to y=2x is

Answer 1

Answer:

4

Step-by-step explanation:

Let (x',y') be the middle point of chord of hyperbola

3$x^{2}$-2$y^{2}$+4x-6y =0

Therefore, Equation of chord is

3xx' - 2yy' + 2(x +x') - 3(y+y')

= 3$x'^{2}$-2$y'^{2}$+4x'-6y'

Chord is parallel to line y=2x, hence

m1=m2= (3x' + 2)/ -(2y' + 3) = 2

3x' - 4y' = 4 => Locus of Middle Point