Question

Prove that the line y=x+3 root 2 touches the circle
x² + y2=9
and find its point of contact
​

Answer 1

Answer:

a line touches the circle, then distance between the centre and line is equal to the radius.

For the circle with centre C(0,0) and r=c

Distance of centre from the line is

d=∣∣∣∣∣∣2−c2∣∣∣∣∣∣

d=∣c∣=r

c=c

is true for all values of c

So, the line touches the circle

y=x+c2    .....(1)

Putting y in the equation of the circle

x2+(x+c2)2=c2

x=2−c,y=2c

are the point of contact.