The equation of the tangent to the circle {x^ | vedclass

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Question

(b) Let the tangent be of form $\frac{x}{{{x_1}}} + \frac{y}{{{y_1}}} = 1$ and area of $\Delta $ formed by it with coordinate axes is

$\frac{1}{2}{

Vedclass · Accepted Answer

$x \pm y = \pm a\sqrt 2 $

Vedclass · Answer

(b) Let the tangent be of form $\frac{x}{{{x_1}}} + \frac{y}{{{y_1}}} = 1$ and area of $\Delta $ formed by it with coordinate axes is

$\frac{1}{2}{x_1}{y_1} = {a^2}$&hellip;.$(i)$

Again, ${y_1}x + {x_1}y - {x_1}{y_1} = 0$

Applying conditions of tangency

$\left| {\frac{{ - {x_1}{y_1}}}{{\sqrt {x_1^2 + y_1^2} }}} \right|\; = a$ or $(x_1^2 + y_1^2) = \frac{{x_1^2y_1^2}}{{{a^2}}}$&hellip;.$(ii)$

From $(i)$ and $(ii)$, we get ${x_1},{y_1}$; which gives equation of tangent as $x \pm y = \pm a\sqrt 2 $.

Trick : There may be $4$ tangents (as in figure).

As the lines $x \pm y = \pm a\sqrt 2 $ make triangle of area &lsquo;$a$&rsquo; in all four quadrants.

The equation of the tangent to the circle ${x^2} + {y^2} = {a^2}$ which makes a triangle of area ${a^2}$ with the co-ordinate axes, is

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