- Home
- Standard 11
- Mathematics
10-2. Parabola, Ellipse, Hyperbola
medium
$y = 2x$ ને સમાંતર અતિવલય $3x^2 - 2y^2 + 4x - 6y = 0$ ની જીવાના મધ્યબિંદુનો બિંદુપથ :
A
$3x - 4y = 4$
B
$3y - 4x + 4 = 0$
C
$4x - 4y = 3$
D
$3x - 4y = 2$
Solution
Let $( G , K )$ be the mid-point of a chord of the hyperbola $3 x ^2-2 y ^2+4 x -6 y =0$.
Then the equation of the chord is
$3 h x-2 k y+2(x+h)-3(y+k)=3 h^2-2 k^2+4 h-6 k \quad$ [using $\quad T=S^{\prime}$ ]
This is parallel to $y =2 x$
$\therefore \quad \frac{-(3 h +2)}{-(2 k +3)}=2 \quad \Rightarrow \quad 3 h +2=4 k +6$
$\Rightarrow \quad 3 h -4 k =4$
Therefore, the locus of $(h, k)$ is $3 x-4 y=4$
Standard 11
Mathematics
