Question

A(-2,2) , B(4,10) are two points in a plane. A circle is drawn with AB diameter .
a). write the equation of the circle
b).Is the circle passes through (-3,3).
c). write the coordinate of the point at which the circle cut the y axis

GUYS PLS GIVE ME CORRECT ANSWERS ....PLS :) VERY URGENT​

Answer 1

Answer:

a)

Equation of circle = (x-x1)(x-2)+(y-y1)(y-y2)=0

⇒ (x+2)(x-4) + (y-2)(y-10)=0

⇒ x² - 2x - 8 + y² - 12 y + 20 = 0

⇒ x² + y² - 2x - 12 y + 12 = 0

b) Putting -3,3 on the circle we get

S1 = 9+9+6-36+12

= 0

Hence (-3,3) lies on the circle.

c) At y axis x=0,

y²-12y + 12=0

⇒ y = (12 ± √144 - 48)/2

⇒ y = 6 ± √24

⇒ y = 6 ± 2√6

Coordinates = (0,6±2√6)