hey guys, a few questions from 2018 mc:
The line 3x − 4y + 3 = 0 is a tangent to a circle with centre (3, −2).
What is the equation of the circle?
A runner has four different pairs of shoes.
If two shoes are selected at random, what is the probability that they will be a matching pair?
A radio telescope has a parabolic dish. The width of the opening is 24 m and the distance
along the axis from the vertex to the opening is 4 m, as shown in the diagram. (attached)
What is the focal length of the parabola?
Hey there!
If a line is tangent to a circle, we know that the distance from the centre to the point of contact is the radius, which meets the tangent at a right angle. Basically, we substitute (3, -2) into the perpendicular distance formula, then use the equation of a circle (x-h)
2+(y-k)
2=r
2 to find the answer (given the centre (h, k)).
When picking the shoes, note that when we pick the first shoe we don't actually care what shoe it is; we just care that the second shoe we pick matches the first one. Hence, once we pick the first shoe, there's only one shoe that matches out of the remaining seven ie. the answer is going to be 1/7.
The last one was addressed already further up the page! (about 5 messages or so up
)
Hope this helps