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Circles

SAT Math· difficulty 4/5

The line y=mxy = mx is tangent to the circle (x−5)2+y2=9(x-5)^2 + y^2 = 9. What is one possible value of mm?

  • A

    34\frac{3}{4}

    check_circle
  • B

    43\frac{4}{3}

  • C

    53\frac{5}{3}

  • D

    35\frac{3}{5}

Explanation

Distance from center (5,0)(5,0) to line mx−y=0mx - y = 0 must equal radius 3: frac∣5m∣sqrtm2+1=3\\frac{|5m|}{\\sqrt{m^2+1}} = 3. So 25m2=9(m2+1)25m^2 = 9(m^2+1), 16m2=916m^2 = 9, m=pmfrac34m = \\pm\\frac{3}{4}.

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