Question

If point p(4,3) q(x,5) are on the circle with centre o(2,3) find the value of x

Answer 1

If two point p and q lie on the circle, That means the distance from the centre must be same because radius never change,

So Distance OP = Distance OQ,

Now let us find the distance and calculate value of x,

The distance formula is :
$\sqrt{ {(x2 \: - \: x1)}^{2} + {(y2 \: - y1)}^{2} }$
You have to take one point as centre and another point as either p or q, and calculate the distance and equal them since radius is equal,

By the way, In calculating distance between two points, You can take any x co-ordinate as x2, and any y co-ordinate as y2,

Distance op = √(4) = 2,

Distance oq = √((2-x)²+4),,

Now equal them,

=> 2 = √((2-x)²+4), Squaring on both the sides,
=> 4 = (2-x)² + 4,
=> (2-x)² = 0,
=> x = 2,

So therefore the value of x is 2,

Hope you understand, Have a great day !

Thanking you,

Bunti 360 !!

Answer 2

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