2 precalculus problems?

Question

I need help with these two problems, please.

Find all points having an x-coordinate of -21 whose distance from the point (-5, -14) is 34.

A hot air balloon is headed due east at an average speed of 6mph at a constant altitude of 190 feet as it crosses an intersection. Find an expression for the distance in d (in feet) from the balloon to the intersection "t" seconds later.

Thank you so much!!

Answer 1

For trhe first problem :

let (-21 ; y) the coordonates of one point

Then the distance is sqrt([- 21 - (- 5)]² + [y - (-14)]²)

so we have (-21 + 5)² + (y + 14)² = 34²

256 + (y + 14)² = 1156

(y + 14)² = 900 = 30²

y + 14 = 30 or y + 14 = -30

y = 16 or y = - 44