Question

Two diametrically opposite points on a circle are (2, 5) and (5, 9), then area of circle is

Answer 1

answer

Since, P(−2,2) and Q(k,0) is the end points of a diameter.

Therefore, mid-point M of PQ=2−2+k,22+0 

i.e., M=(2k−1,1)

Also, MP= radius of circle

Thus (−2−2k+1)2+(2−1)2=1

⇒(−1−2k)2+1=1

⇒1+4k2+K+1=1

⇒k2+4k+4=0

⇒(k+2)2=0

⇒k=−2

Therefore, mid-point M=(−22−1,1)=(−2,1) which is 

equal to the centre of circle.

Hence, equation of circle is 

(x+2)2+(y−1)2=12

Step-by-step explanation:

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Answer 2

Answer: 19.642

Step-by-step explanation:

Distance = $\sqrt{ (x_{1} - x_{2})^{2} + (y_{1} - y_{2})\\^{2}$

$\sqrt{(2-5)^{2} + (9-5)^{2}$

$\sqrt{9+16\\}$

5

radius of circle = 2.5

area of circle= 22/7 x 2.5 x 2.5

= 19.642