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Question

Find the equations of those tangents to the circle x2+y2=52 which are parallel to the straight line 2x+3y=6.

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Solution

Equation of the tangent to the circle is given by
y=mx±a1+m2
In this case, a=52=213 and m=23

equations of tangent are
y=23x±213×1+49

3y+2x=±2(13)=±26

3y+2x=26 and 3y+2x=26 are the equations of tangents.

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