A planet follows an elliptical path described by 16 x squared + 4 y squared = 64. A comet follows the parabolic path y equals x squared minus 4. Where might the comet intersect the orbiting planet?

The comet might intersect the orbiting planet at (0, -4),.

Step-by-step explanation:

Given that, a planet follows an elliptical path described by

.........(1)

A comet follows the parabolic path

.........(2)

To find the intersecting point, we need to solve the above equations.

Putting    in the equation (1)

When y = -4 , then

When , then

The comet might intersect the orbiting planet at (0, -4),.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

a

step-by-step explanation: