Question

Question is in attachment

uttam if u r not busy
send me this answer
if not it's ok
it's not important for me now
network proper ga vachaka
post chey uttam

no problem​

Answer 1

Answer:

$\mathrm{Area = \dfrac{1}{2}\bigg(\dfrac{a^2}{x_1}\bigg)\bigg(\dfrac{a^2}{y_1}\bigg)}$

Step-by-step explanation:

Given :

x² + y² = a² is a circle.

P(x₁, y₁) is a point on the circle through which a tangent is drawn

To find :

The area of the triangle formed with tangent and the coordinate axes

Solution :

Circle equation : x² + y² = a²

We know that, if a point (x₁, y₁) is a point on the circle through which a tangent is drawn, then equation of tangent is x₁x + y₁y = a²

So,

$\implies \mathrm{\dfrac{x_1x}{a^2} + \dfrac{y_1y}{a^2} = 1}$

$\implies \mathrm{\dfrac{x}{\bigg(\dfrac{a^2}{x_1}\bigg)} + \dfrac{y}{\bigg(\dfrac{a^2}{y_1}\bigg)} = 1}$

This is of the form $\boxed{\mathrm{\dfrac{x}{a} + \dfrac{y}{b} = 1}}$ [Line - intercept form]

Here a, b are intercepts

We know that,

Area formed by the line intercept form is

$\boxed{\mathrm{A = \dfrac{1}{2}|ab|}}$

Here,

$\mathrm{a = \dfrac{a^2}{x_1} ; b = \dfrac{a^2}{y_1}}$

So,

$\implies \mathrm{A = \dfrac{1}{2}\bigg(\dfrac{a^2}{x_1}\bigg)\bigg(\dfrac{a^2}{y_1}\bigg)}$

$\therefore \underline{\boxed{\mathbf{A = \dfrac{1}{2}\bigg(\dfrac{a^4}{x_1y_1}\bigg)}}}$

Hope it helps!!