Question

If a point p has co-ordinates (0, −2) and q is any point on the circle, x 2+y 2−5x−y+5=0, then the maximum value of (pq)2 is

Answer 1

Answer:

The maximum value of PQ² = 14 + 5√3

Step-by-step explanation:

From the given eqn of the circle = x² + y² -5x - y +5 = 0,

the center of the circle is at (5/2 , 1/2) and the radius is

√[(5/2)² + (1/2)² - 5]

= √[25/4 + 1/4 -5]

= √[26-20/4]

= √3/√2

Since this point lies outside of the circle hence the maximum distance would be along the straight line joining the point and radius.

Let O be the center then the maximum distance is,

PO + radius

Now,

PO = √[(5/2-0)² + (1/2 +2)²]

= √[25/4 + 25/4]

= 5/√2

Hence PQ = PO + r

=> PQ² = (PO + r)²

= (5/√2  +  √3/√2)²

= 25/2  + 3/2  + 5√3

= 14 + 5√3

Answer 2

Answer:

S

Step-by-step explanation:

You are correct bro

Super