## Circles

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: C

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

The slope m of a tangent through the point (7, 1) to the circle x2+y2=25 satisfies the equation

**Options:**

A. | 12m2 + 7m - 12 = 0 |

B. | 12m2 + 7m + 9 = 0 |

C. | 12m2 - 7m - 12 = 0 |

D. | 9m2 + 12m + 16 = 0 |

**Answer: Option C**

: C

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

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