NDA 2023 Maths · Mathematics · Circles · medium

The line y=mx+4 touches the circle x^2+y^2=8. The possible values of m are

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The line

y=mx+4

touches the circle

x^2+y^2=8

. The possible values of

m

are

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Answer: (D) $\pm1$

Tangency requires the distance of the centre from the line to equal the radius:

\dfrac{4}{\sqrt{1+m^2}}=2\sqrt2

, so

16=8(1+m^2)

, giving

m^2=1

. Both signs are valid by symmetry;

\pm\sqrt2

results from a slip in squaring the radius.

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