Originally Posted by

**afeasfaerw23231233** p143 q9 c

I have problem in (c). I get the answer 2x+y = 0 but the book says it is 2x+3y = 0

question:

consider an ellipse E:$\displaystyle \frac {x^2}9 + \frac {y^2}4 = 1$

and a line L :$\displaystyle 2x-3x+6=0$ **I assume that you mean: 2x-3y+6=0**

and D: $\displaystyle y=mx+c$ is a line parallel to L.

a) if D cuts E at $\displaystyle Q(x_1 , y_1) $and $\displaystyle R(x_2 , y_2)$ , show that $\displaystyle x_1$ and $\displaystyle x_2$ are the roots of the equation

$\displaystyle 8x^2 +12cx + 9c^2- 36=0$

b) find the range of values of c if E and D cut at (i) 2 points / (ii) 1 point

c) M is the mid - point of QR. Find the equation of the locus M as c varies.

here's my working in (c)

$\displaystyle D: y = - \frac 2 3 x + c $

$\displaystyle x_1 + x_2 = - \frac {12c}8 = - \frac {3c}2 $

$\displaystyle x = - \frac {3c}4$

$\displaystyle y_1 +y_2 = - \frac 2 3 (x_1 +x_2) + 2x = 3c $

$\displaystyle y= \frac 3 2 c = -2 x $

2x+y = 0

but answer says it's 2x+3y=0. what's wrong??? thanks!