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Question

The angle between the tangents drawn at the points (5,12)and (12,-5) to the circles x2+y2=169 is


A

45°

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B

60°

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C

30°

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D

90°

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Solution

The correct option is D

90°


Explanation for the correct option:

Given the equation of the circle : x2+y2=169

Differentiating with respect to x we get,

2x+2ydydx=0dydx=-xy

For m1

dydx(5,12)=-512

For m2

dydx(12,-5)=125

We know that if m1m2=-1 then the lines will be perpendicular, so

-512125=-1

This proves that the angle between the tangents is 90°

Hence, the correct option is (D).


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