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If a chord of a circle $x^{2} + y^{2} = 25$ with one
extremity at $(4, 3)$ subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be

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(−3,−4)

(4,−3)

(3,4)

(−3,4)

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detailed solution

Correct option is D

Let P be the point (4, 3) and Q (h, k) be the other extremity of the chord through P. Centre of the circle is the origin 0. Then OP is perpendicular to OQ⇒kh×34=−1⇒kh=−43which is satisfied by (h,k)=(−3,4)

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If a chord of a circle x2+y2=25 with one extremity at (4,3) subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be

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Ready to Test Your Skills?

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If a chord of a circle $x^{2} + y^{2} = 25$ with one
extremity at $(4, 3)$ subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be