a quick geo problem pls helpppp

Question

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446

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+125

The line 2y=3x intersects the ellipse $\frac{x^2}{8} + \frac{y^2}{18} = 1$ at the points $Q$ and $R$ , what is the length of segment QR?

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Mathlord Nov 15, 2021

geno3141 · Answer 1 · 2021-11-15T02:53:27

2y = 3x ---> y = (3/2)x

x² / 8 + y² / 18 = 1 ---> x² / 8 + [(3/2) x ]² / 18 = 1

---> x² / 8 + (9/4) x² / 18 = 1

---> x² / 8 + 9 x² / 72 = 1

---> 9 x² + 9 x² = 72

---> 18 x² = 72

---> x² = 4

---> x = 2 ---> y = 3 ---> (2, 3)

---> x = -2 ---> y = -3 ---> (-2, -3)

Now, use the distance formula to find the distance between these two points.