Answer
$0.54$ astronomical units (which is $\approx51$ million miles)
Work Step by Step
We have $ r=\dfrac{1.069}{1+0.967 \sin \theta}$
or, $ r=\dfrac{1.069}{1+0.967 \sin (\dfrac{\pi}{2})}$
(we use $\theta=\pi/2$ for the shortest distance from the Sun.)
or, $ r \approx 0.54$ astronomical units
