# Conic Sections: Circles

## Conic Sections: Circles Study Guide: Homework Help

Where do the graphs of x+y=65 and x^2+y^2=194 cross (if they cross)?

We have the equations 1) `x + y = 65` 2) `x^2 + y^2 = 194` Solve the first equation for y: `y = 65 - x` Substituting into the second equation we obtain `x^2 + (65-x)^2 = 194` ` `which implies that `x^2 + 65^2 - 2(65)x + x^2 - 194 = 0` `implies`  `2x^2 -130x + 4031 = 0` Using the...

What is the equation of a circle with diameter AB; A is (5,4) and B is (-1,-4)?

First calculate the radius of the circle: The horizontal distance between the points is the distance between the x coordinates of A and B, |5| + |-1| = 6, and the vertical distance is the distance between the y coordinates of A and B, |4| + |-4| = 8 The diameter is then the direct distance...

Since we have learned in geometry that angle in semi circle is right angle. Apply this result and can calculate equation of circle. Let P(x,y) be any point on the circle.Thus A(5,4),B(-1,-4) and P(x,y) on the circle. Also PA is perpendicular to PB. slope of PA=(y-4)/(x-5) slope of PB=(y+4)/(x+1)...