Question

If the line lx + my = 1 is a tangent to the circle x² + y² = a², then the point (l, m) lies on a circle.

पर्याय

• True

• False

Answer 1

This statement is True.

Explanation:

Given equation of circle is x² + y² = a²

And the tangent is lx + my = 1

Here centre is (0, 0) and radius = a

If (l, m) lies on the circle

∴ `sqrt((l - 0)^2 + (m - 0)^2 = a`

⇒ `sqrt(l^2 + m^2) = a`

⇒ `l^2 + m^2 = a^2`   .....(Which is a circle)

So, the point (l, m) lies on the circle.