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10-1.Circle and System of Circles
easy
The equation of the tangent at the point $\left( {\frac{{a{b^2}}}{{{a^2} + {b^2}}},\frac{{{a^2}b}}{{{a^2} + {b^2}}}} \right)$ of the circle ${x^2} + {y^2} = \frac{{{a^2}{b^2}}}{{{a^2} + {b^2}}} $ is
A
$\frac{x}{a} + \frac{y}{b} = 1$
B
$\frac{x}{a} + \frac{y}{b} + 1 = 0$
C
$\frac{x}{a} - \frac{y}{b} = 1$
D
$\frac{x}{a} - \frac{y}{b} + 1 = 0$
Solution
(a) From formula of tangent at a point,
$x\left( {\frac{{a{b^2}}}{{{a^2} + {b^2}}}} \right) + y\left( {\frac{{{a^2}b}}{{{a^2} + {b^2}}}} \right) $
$= \frac{{{a^2}{b^2}}}{{{a^2} + {b^2}}} $
$\Rightarrow \frac{x}{a} + \frac{y}{b} = 1$.
Standard 11
Mathematics
