Question

DIE
- PQ is a tangent to the circle, centre C, with
equation x + y2 + 6x – 8y = 0.

a) Find the length of CQ.
P has coordinates (3,-4).
b) Find the length of PQ.
c) Calculate the length of the shortest
distance from P to the circle.​

Answer 1

Answer:

Step-by-step explanation:

Given circles are

S  

1

​  

:x  

2

+y  

2

+6x+8y+a=0   ...(1)

and S  

2

​  

:x  

2

+y  

2

+2x−6y−b=0    ...(2)

The equation of common chord of the two circles is

S  

1

​  

−S  

2

​  

=0⇒4x+14y+(a+b)=0   ...(3)

Since the circle S  

1

​  

 bisects the circumference of the circle S  

2

​  

, therefore, (1) passes through the center of the circle S  

1

​  

 i.e. (−1,3)

∴4(−1)+14(3)+a+b=0⇒a+b=−38