Question

A(1,0) B (7,0) are two points on x axis. A point P is taken in the first quadrant such that PAB is an isosceles triangle and PA = PB = 5 units. Find the equation of the circle described on PA as diameter.

Answer 1

Answer:

( x - 2.5 )² + ( y - 2 )² = 6.25

Step-by-step explanation:

Let's assume that there is a point Q which has coordinates ( 0, 4 ). Then PQ is the height of the isosceles triangle PAB.

PQ = √5² - 3² = 4

So The coordinates of P are ( 4, 4 ).

PA is a diameter of the circle and r = 5/2 = 2.5

Also the coordinates of the center are:

p = ( 4 + 1 ) / 2 = 2.5

q = ( 4 + 0 ) / 2 = 2

Finally the equation of the circle is :

( x - p )² + ( y - q )² = r²

( x - 2.5 )² + ( y - 2 )² = 6.25