AM-120

Line meeting a curve

A Math · Secondary 3 · Hard · Line meeting a curve

The line with equation

3x-y=5

cuts the curve

x^2+4y^2-9=0

at points

P

and

Q

. Find the coordinates of

P

and

Q

.

$(1,-2)$ and $\left(\tfrac{91}{37},\tfrac{98}{37}\right)$
$(1,2)$ and $\left(\tfrac{91}{37},-\tfrac{98}{37}\right)$
$(2,-1)$ and $\left(\tfrac{98}{37},\tfrac{91}{37}\right)$
$(-1,2)$ and $\left(-\tfrac{91}{37},\tfrac{98}{37}\right)$

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