The slope m of a tangent through the point (7, 1) to the circle x2+y2=25 satisfies the equation
A
12m2 + 7m - 12 = 0
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B
12m2 + 7m + 9 = 0
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C
12m2 - 7m - 12 = 0
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D
9m2 + 12m + 16 = 0
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Solution
The correct option is C12m2 - 7m - 12 = 0 Equation of a tangent to x2+y2 = 25 is y = mx ± 5√1+m2
This passes through (7, 1) ⇒ 1 = 7m ± 5√1+m2 ⇒(1−7m)2=25(1+m2)⇒49m2−14m+1=25+25m2⇒24m2−14m−14=0 ⇒12m2 - 7m - 12 = 0