Question

if the points p(5,3) and Q ( k,4) are on a circle with center O(2,-1) find 5he value of k​

Answer 1

Points P and Q are on the circle. That means the distance of both the points from the centre is same

Therefore,

OP = OQ

√(5 - 2)² + (3 -(-1))² = √(k - 2)² + (4-(-1))²

Squaring on both the sides cancels the roots.

(5-2)² + (3+1)² = (k-2)² + (4+1)²

3² + 4² = (k-2)² + 5²

9 + 16 = (k-2)² +25

25 - 25 = (k-2)²

(k-2)² = 0

k-2 = 0

k = 2.

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